Green’s Dictionary of Slang

1. (Aus.) a derog. term for a black or Asian person [rhy. sl. = wog n.¹ (1)].

1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 24: Dapto Dog Wog.
1999		G. Seal Lingo 90: Some other examples: [...] dapto dog for wog (usually just a dapto), from the famous New South Wales dog races, the Dapto Dogs.
2013		T. Peacock More You Bet 11: ‘Dapto dogs’ has lent its name as rhyming slang for the derogatory term ‘wogs’.

2. (Aus.) a particularly unattractive girl [dog n.² (8)].

1993

Aus. Word Map 🌐 Dapto dog [...] ‘The Dapto Dog was always reference to being a particularly ugly girl’.