Granted collecting in Australia got going very late, but I also wonder whether the lack of ballads from there is because of the migration history. We think of the Appalachian Mountains as a hotbed of Child Ballads (Cecil Sharp was finding plenty of versions of 'Young Hunting', 'Two Sisters', 'Lord Thomas and Fair Ellender' and 'The Housecarpenter' in 1916), but the circumstances of that community were pretty unique. The so-called 'Scotch-Irish' were arriving in America by the middle of the 18th century, up to a hundred years before the main migration to Australia. Many of them had been transplanted to Ulster a hundred years before that, and my guess is that the Appalachian ballads present - at least to some degree - a snapshot of repertoire popular in Lowland Scotland and Northern England in the 17th century. Also of course the communities were very isolated, so the songs survived.

So perhaps by the time emigration to Australia really got going, those ballads were already falling from popularity in the old country. Also I suspect the Scots influence was smaller than in the Appalachians.