Green’s Dictionary of Slang

(Aus.) a young woman.

1941		Baker Popular Dict. Aus. Sl.
1942		Yank 4 Nov. 20/3: A shikkered wooloomooloo yank [...] met a wowsere with two ding dong sninnies.
1944		P. Kendall Dict. Service Sl. n.p.: sninny . . . a young girl.
1949		Argus (Melbourne) 1 Oct. 11/3: There may be students of Australiana who are familiar with all these expressions, but I for one admit I am baffled by many. I did not know, for example, that a sheila is also a sninny. If the same sninny is of elegant proportions and gets into a cossie she looks ribuck, meaning that she is most attractive in a swimming costume.