Hi Nimsy,
I can't comment on the public system, but from previous commentary by various members, it seems to be a bit different from State to State. You might get some more targeted info by identifying which town/city you would go to.
If you chose to go private, you should get a fairly accurate estimate of out-of-pockets beforehand from your plastic surgeon/health fund. My out-of-pocket estimates for a private reconstruction were pretty accurate, except for an unexpected $800-odd pathology bill for bloods and other tests while I was in ICU.
Very best wishes
Megan