Green’s Dictionary of Slang

to move, to go, to wander.

1923		Wodehouse Inimitable Jeeves 135: I borrowed a bicycle [...] and toodled off.
1945		G. Fairlie Capt. Bulldog Drummond 177: I toodled up to the sleepy countryside round Bayswater.
1960		B. Kops Dream of Peter Mann Act II: Take my advice and toodle loo.
1997		(con. 1960s) A. Frewin London Blues 242: I must be toodling off now.