1670s in modern sense of "short pleasure trip," earlier "tiresome journey" (1590s), from jaunt (v.).
"tire (a horse) by riding back and forth on it, ride hard," 1560s, of unknown origin, "the word being confused with other words of similar or related meanings" [Century Dictionary]. Not found in Middle English, perhaps from some obscure French word. Also "be jolted or shaken up" (1570s), main modern sense "wander here and there for pleasure" is from 1640s. Related: Jaunted; jaunting.