Hi there,
The Special Allowance (not called a Housing Allowance for tax reasons) is available for those who can prove that their social ties are to their home country. This is a really ambiguous term and what they require as proof seems to change from person to person.
I didn't receive the SA initially as they wanted more 'proof'. When I asked what more proof I could provide (I sent in stuff related to my business back in the UK, bills, other bits and bobs), they said that things related to my primary or secondary schooling in the UK would be enough. I then sent them copies of class photos from primary school and GCSE/A Level school reports and that was accepted.
I think if you did your schooling in Oz, even if you have family here, you should be fine. I'm a PR here, married to a local, got married here, have had two kids here, did uni here etc etc etc and I was approved.
Hope this helps!