Online Etymology Dictionary

Q: 16th letter of the classical Roman alphabet, from the Phoenician equivalent of Hebrew koph, which was used for the more guttural of the two "k" sounds in Semitic.

The letter existed in Greek, but was little used and not alphabetized; the stereotypical connection with -u- began in Latin. Anglo-Saxon scribes adopted the habit at first, but later used spellings with cw- or cu-. The qu- pattern returned to English with the Norman Conquest. Scholars use -q- alone to transliterate Semitic koph (e.g. Quran, Qatar, Iraq ).

In Christian theology, Q has been used since 1901 to signify the hypothetical source of passages shared by Matthew and Luke, but not in Mark; probably it is an abbreviation of German Quelle "source."
Q and A: also Q & A, 1954, abbreviation of question and answer (itself attested by 1817).
Q.E.D.: 1760, abbreviation of Latin quod erat demonstrandum "which was to be demonstrated."
q.t. (n.): slang for "quiet," in phrase on the q.t., attested from 1874. Phrase on the quiet appears from 1847.
qi (n.): "physical life force," 1850, from Chinese qi "air, breath."
qua: "as, in the capacity of," from Latin qua, ablative singular fem. of qui "who," from PIE *kwo-, stem of relative and interrogative pronouns (cf. Old English hwa "who," hwæt "what;" Gothic hvas "who;" Greek posos "how much?"); see who.
quaalude (n.): 1965, proprietary name (trademark by Wm. H. Rohrer Inc., Ft. Washington, Pennsylvania, U.S.A.) of methaqualone.
quab (n.): "sea-slug," 1610s, from Middle Dutch or Middle Low German quabbe (Dutch kwab).
quack (v.): "to make a duck sound," 1610s, quelke, of echoic origin (cf. Middle Dutch quacken, Old Church Slavonic kvakati, Latin coaxare "to croak," Greek koax "the croaking of frogs," Hittite akuwakuwash "frog"). Middle English on the quakke (14c.) meant "hoarse, croaking." Related: Quacked; quacking.
quack (n.): "medical charlatan," 1630s, short for quacksalver (1570s), from Dutch kwaksalver, literally "hawker of salve," from Middle Dutch quacken "to brag, boast," literally "to croak" (see quack (v.)) + zalf "salve" (see salve (v.)). Cf. German Quacksalber, Danish kvaksalver, Swedish kvacksalvare.
quackery (n.): c.1710, from quack (n.) + -ery.
quad: 1820 as a shortening of quadrangle; 1896 as quadruplet; 1970 as quadraphonic. Related: Quads.
quadrangle (n.): late 14c., from Old French quadrangle (13c.), from Late Latin quadrangulum "four-sided figure," properly neuter of Latin adjective quadrangulus "having four quarters," from Latin quattuor "four" (see four) + angulus "angle" (see angle (n.)). The shortened form quad for "quadrangle of a college," is first recorded 1820 in Oxford slang.
quadrangular (adj.): early 15c., from Medieval Latin quadrangularis, from Late Latin quadrangulum (see quadrangle).
quadrant (n.): late 14c., "a quarter of a day, six hours," from Latin quadrantem (nominative quadrans) "fourth part," noun use of present participle of quadrare "to make square," from quadrus "a square," from quattuor "four" (see four). The surveying instrument is first so called c.1400, because it forms a quarter circle.
quadraphonic (adj.): 1969, irregular formation from quadri- "four" + phonic, from Greek phone "sound, voice" (see fame (n.)). The goal was to reproduce front-to-back sound distribution in addition to side-to-side stereo.
quadratic (adj.): 1650s, "square," from quadrate (late 14c.), from Latin quadratus "square," past participle of quadrare "to square," related to quattuor "four" (see four). Quadratic equations (1660s) so called because they involve the square of x.
quadrennial (adj.): 1650s, "lasting four years;" as "happening every four years," 1701; from quadri- + ending from biennial, etc. Correct formation would be *quadriennial Related: Quadrennially.
quadri-: before vowels quad-, word-forming element meaning "four, four times," from Latin quadri-, related to quattor "four" (see four).
quadricep (n.): 1840, from quadri- on model of bicep. Related: Quadriceps.
quadrilateral (n.): 1640s, from Latin quadrilaterus, from quadri- "four" (see quadri-) + latus (genitive lateris) "side" (see oblate (n.)). Related: Quadrilaterally.
quadrille (n.): 1773, "lively square dance for four couples," from French quadrille, originally one of four groups of horsemen in a tournament (a sense attested in English from 1738), from Spanish cuadrilla, diminutive of cuadro "four-sided battle square," from Latin quadrum "a square," related to quattuor "four" (see four). The craze for the dance hit England in 1816, and it underwent a vigorous revival late 19c. among the middle classes. Earlier a popular card game for four hands (1726).
Quadrille began to take the place of ombre as the fashionable card game about 1726, and was in turn superseded by whist. [OED]
quadrillion (n.): 1670s, from French quadrillion (16c.) from quadri- "four" (see quadri-) + (m)illion. Cf. billion. In Great Britain, the fourth power of a million (1 followed by 24 zeroes); in the U.S., the fifth power of a thousand (1 followed by 15 zeroes).
quadriplegia (n.): 1895, from quadri- + ending from paraplegia.
quadriplegic (adj.): also quadraplegic, 1897, a medical hybrid coined from Latin-based quadri- "four" + -plegic, as in paraplegic; ultimately from Greek plege "stroke," from root of plessein "to strike" (see plague (n.)). A correct, all-Greek formation would be *tessaraplegic. The noun is first attested 1912, from the adjective.
quadroon (n.): 1707, "offspring of a white and a mulatto," from Spanish cuarteron (used chiefly of the offspring of a European and a mestizo), from cuarto "fourth," from Latin quartus (see quart), so called because he or she has one quarter African blood. Altered by influence of words in quadr-.
quadruped (n.): 1610s (implied in quadrupedal), from French quadrupède, from Middle French, from Latin quadrupes (genitive quadrupedis) "four-footed, a four-footed animal," from quadri- "four" (see quadri-) + pes "foot" (see foot (n.)). The adjective is attested from 1741.
quadruple (v.): late 14c., from Latin quadruplare "make fourfold," from quadruplus (n.) "quadruple," from quadri- "four" (see quadri-) + -plus "fold" (see plus).
quadruplet (n.): "one of four children at a single birth," 1787; see quadruple. Related: Quadruplets. Musical sense is from 1873.
quaere: Latin imperative of quaerere "to ask, inquire" (see query (v.)). Hence "one may ask" (1530s).
quaff (v.): 1510s (implied in quaffer), perhaps imitative, or perhaps from Low German quassen "to overindulge (in food and drink)," with -ss- misread as -ff-. Related: Quaffed; quaffing. The noun is from 1570s.
quag (n.): "marshy spot," 1580s, a variant of Middle English quabbe "a marsh, bog," from Old English *cwabba "shake, tremble" (like something soft and flabby).
quagga (n.): 1785, from Afrikaans (1710), from the name for the beast in a native language, perhaps Hottentot quacha, probably of imitative origin. In modern Xhosa, the form is iqwara, with a clicking -q-. The last one died in an Amsterdam zoo in 1883.
quagmire (n.): 1570s, from obsolete quag "bog, marsh" + mire (n.). Extended sense of "difficult situation, inextricable position" is recorded by 1766.
quahog (n.): 1753, from an Algonquian language, perhaps Narragansett poquauhock or Pequot p'quaghhaug "hard clam."
quai (n.): 1870, from French quai (see quay). Often short for Quai D'Orsay, street on the south bank of the Seine in Paris, site of the French Ministry of Foreign Affairs and sometimes used metonymically for it (1922).
quail (n.): c.1300, quayle, from Old French quaille, perhaps via Medieval Latin quaccula (cf. Provençal calha, Italian quaglia, Old Spanish coalla), from a Germanic source (cf. Old High German quahtala "quail," German Wachtel), imitative of the bird's cry. Or the English word might be directly from Germanic. Slang meaning "young attractive woman" first recorded 1859.
quail (v.): "to lose heart, to shrink," c.1400, of unknown origin, perhaps from Middle Dutch quelen "to suffer, be ill," from Proto-Germanic *kwel- "to die" (see quell). Or from obsolete quail "to curdle" (late 14c.), from Old French coailler, from Latin coagulare (see coagulate). Sense of "cower" is attested from 1550s. Common 1520-1650, then rare until 19c.; apparently revived by Scott. Related: Quailed; quailing.
quaint (adj.): early 13c., "cunning, proud, ingenious," from Old French cointe "pretty, clever, knowing," from Latin cognitus "known," past participle of cognoscere "get or come to know well" (see cognizance).

Sense of "old-fashioned but charming" is first attested 1795, and could describe the word itself, which had become rare after c.1700 (though it soon recovered popularity in this secondary sense). Chaucer used quaint and queynte as spellings of cunt in "Canterbury Tales" (c.1386), and Andrew Marvell may be punning on it similarly in "To His Coy Mistress" (1650). Related: Quaintly; quaintness.
quake (v.): Old English cwacian "quake, tremble, chatter (of teeth)," related to cweccan "to shake, swing, move, vibrate," of unknown origin with no certain cognates outside English. Perhaps somehow imitative. Related: Quaked; quaking. The noun is attested from c.1400, originally "a trembling in fear," but was rare except in combinations.
Quaker (n.): 1651, said to have been applied to them in 1650 by Justice Bennett at Derby, from George Fox's admonition to his followers to "tremble at the Word of the Lord;" but the word was used earlier of foreign sects given to fits of shaking during religious fervor, and that is likely the source here. Either way, it was never an official name of the Religious Society of Friends. The word in a literal sense is attested from early 15c. Quaker gun (1809, American English) was a log painted black and propped up to look from a distance like a cannon, so called for the sect's noted pacifism. Philadelphia has been known as the Quaker City since at least 1824.
quale (n.): "death, destruction," Old English cwalu, cognate with Old Norse kval "torment, torture," from a variant of the root of quell.
qualification (n.): 1540s, "restriction, modification," from Medieval Latin qualificationem (nominative qualificatio), noun of action from past participle stem of qualificare (see qualify). Meaning "accomplishment that qualifies someone to do something" is from 1660s; that of "necessary precondition" is from 1723. Related: Qualifications.
qualifier (n.): 1560s, agent noun from qualify. Grammatical sense is from 1580s.
qualify (v.): mid-15c., "to invest with a quality," from Medieval Latin qualificare "attribute a quality to," from Latin qualis "of what sort" (see quality) + facere "to make" (see factitious). Sense of "be fit for a job" first appeared 1580s. Related: Qualified; qualifying.
qualitative (adj.): early 15c., from Late Latin qualitativus, from Latin qualitas (see quality). Related: Qualitatively.
quality (n.): c.1300, "temperament, character, disposition," from Old French qualite (12c., Modern French qualité), from Latin qualitatem (nominative qualitas; said to have been coined by Cicero to translate Greek poiotes), from qualis "of what sort," from PIE pronomial base *kwo- (see qua). Meaning "degree of goodness" is late 14c. Meaning "social rank, position" is c.1400. Noun phrase quality time first recorded 1977. Quality of life is from 1943. Quality control first attested 1935.
qualm (n.): Old English cwealm (West Saxon) "death, disaster, plague," utcualm (Anglian) "utter destruction," related to cwellan "to kill," cwelan "to die" (see quell). Sense softened to "feeling of faintness" 1520s; meaning "uneasiness, doubt" is from 1550s; that of "scruple of conscience" is 1640s.

A direct connection between the Old English and modern senses is wanting, but it is nonetheless plausible, via the notion of "fit of sickness." The other suggested etymology, less satisfying, is from Dutch kwalm "steam, vapor, mist," which also may be ultimately from the same Germanic root as quell.
qualms (n.): see qualm.
quandary (n.): 1570s, "state of perplexity," of unknown origin, perhaps a quasi-Latinism based on Latin quando "when."