Green’s Dictionary of Slang

(Aus.) to wander around.

1902

Bulletin (Sydney) 26 July 28/2: Encountered Melbourne’s peripatetic swaggie, who used to wallaby round the city day after day, t’other afternoon, and hardly recognised him. [...] He was in his right mind, and clothed in a black flogger, light pants and bell-topper – all somewhat dilapidated but still passable.