Green’s Dictionary of Slang

1. money, esp. money set aside for use in betting.

1949		L. Glassop Lucky Palmer 36: Two quid? Break it down. That’s me willie. That’s all I got.
1975		Bulletin (Sydney) 26 Apr. 45: Anyway, we get this dead set sneak go for a willy in a supermarket.
1989		R. McDonald Rough Wallaby 219: Mugs poised to slip the bookies a ‘willie.’.

2. a wallet.

1953		Argus (Melbourne) 31 Oct. 9/6: The ‘rip-and-tear man’ usually works with a ‘bumper-up’ - someone who bumps the victim off balance and distracts his attention while the pickpocket ‘lifts’ the ‘willy’ (wallet)’.
1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxiv 4/3: dip in willy: Steal from a person’s pocket. [Ibid.] xliii 11/3: willy: A wallet.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 9: He wasted no time in diving into his burrow and extracting his willy.