I would be inclined to agree with you and your source. Words associated with Aborigines are not necessarily native: tucker, walkabout, damper, and I have grave doubts about gin 'woman' since Aboriginal words aren't monosyllabic. But it is always possible that they could have borrowed a word for 'fun'

My source is the Pocket Oxford Dictionary, which has an appendix of Australian/NZ terms. It laconically marks it "[Ab.]". This is not much use for tracking down which one of two hundred odd languages it might come from.