Green’s Dictionary of Slang

toddle n.

a promenade, made for social purposes to show oneself, meet friends, etc.

[UK]Bristol Magpie 27 July 6/1: [T]he many elegancies, who daily ‘do’ the Queen's Road ‘crawl,’ Park Street ‘trot,’ and Clare Street ‘toddle ’.

In phrases

on the toddle [toddle v.]

on the move; walking along.

[UK]Egan Life in London (1869) 268: After one or two more flashes of lightning, the trio were again on the toddle.
[UK]Henley & Stevenson Deacon Brodie I tab.I v: You and me had best be on the toddle.