"a fancy dish in cookery" (especially a non-native one), late 16c., earlier quelk-chose from English pronunciation of French quelque chose "a something, a little something." Quelque is from Latin qualis "of what kind?" (from PIE root *kwo-, stem of relative and interrogative pronouns).
also kicksy-wicksy, ludicrous or loving term for "wife" in Shakespeare ("All's Well," II iii.297), 1601, perhaps a perversion of kickshaw "a fancy dish in cookery."
also *kwi-, Proto-Indo-European root, stem of relative and interrogative pronouns.
It forms all or part of: cheese (n.2) "a big thing;" cue (n.1) "stage direction;" either; hidalgo; how; kickshaw; neither; neuter; qua; quality; quandary; quantity; quasar; quasi; quasi-; query; quib; quibble; quiddity; quidnunc; quip; quodlibet; quondam; quorum; quote; quotidian; quotient; ubi; ubiquity; what; when; whence; where; whether; which; whither; who; whoever; whom; whose; why.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kah "who, which;" Avestan ko, Hittite kuish "who;" Latin quis/quid "in what respect, to what extent; how, why," qua "where, which way," qui/quae/quod "who, which;" Lithuanian kas "who;" Old Church Slavonic kuto, Russian kto "who;" Old Irish ce, Welsh pwy "who;" Old English hwa, hwæt, hwær, etc.