You most definitely can have this surgery publicly. I am not sure of Sydney surgeons names but many surgeons operate both publicly and privately. What some ladies do is call the surgeons rooms and ask if they do public as well as private. You can then have a private consult which you would have to pay for but then ask to go on their public list. Some ladies actually go for a few consults this way to find a surgeon they are comfortable with.
Pop over to the recon group and have a look through the DIEP photo stories.
Paula x