Green’s Dictionary of Slang

(Aus.) a woman, a girlfriend.

1948		Smith’s Wkly (Sydney) 25 Dec. 6/2: Anyway, it was around about this time the Crow started tracking square with a potato peeler — which [...] you will find rhymes with sheila, and means the same thing. This potato was a funny bit of furniture known as May-I.
1959		D. Niland Gold in the Streets 64: ‘He got hold of a potater. He’ll see us later.’ ‘Any good?’ Danno whispered. ‘Who?’ ‘The sheila.’.
1963–74		B. Humphries Barry McKenzie [comic strip] in Complete Barry McKenzie (1988) 77: It strikes me he’s been endeavouring to commit intimacy with your potato.
1970		G. Greer Female Eunuch 266: Who likes to be called dry-goods, a potato, a tomato or a rutabaga?
1999		G. Seal Lingo 89: Another rhyming slang term for sheila is potato peeler.