'Well, I won't have you jauntering about with her any more!' said Sherry, in a very imperious style. 'Mind that!' —Georgette Heyer, Friday's Child
Not in OED (in any sense), but there are ghits and Google Books hits showing it going back some time; as a verb, usually construed with 'about'. I can't tell if it's from a particular regional dialect. Also occurs as a noun, synonym of 'jaunt'. Also of course an agent noun formed from 'jaunt'.