Czech citizen wanting to give birth in Australia

Hi,

Im an Australian born Australian citizen,40, male. I live in Indonesia with my defacto partenr of 6 years, Czech, 33, female.
We have lived and worked overseas for the last 10 years, so I am a non resident for taxation purposes (in Australia).
We recently found out we are pregnant, and want to return to Australia to have the child. All my family is still in australia, so we have a place to stay there on the Sunshine Coast in queensland.
We are not legally wed.
My partner has been to Australia with me previously 3 times.

The baby is due Feb 16 2013. We recently applied for a spouse visa, have paid the application money and are now waiting for this to be processed, but it will take another 11 month....not in time for the baby. So we are exploring other options (eg medical visa, standard E-visa). Anyhow i dont think getting into the country to have the baby will be the problem at all.

What we dont know is whether we can use the public health system in Australia when we get there.

Does anyone know the rules about this? 

Is it possible? How we do go about it? Does the fact that I am Australian help this issue?
We will have all the results of prior medical examinations in the country we presently live in eg ultra sounds, check ups, results, etc etc.
We can get quite good care where we currently live (Indonesia), but being that the baby will be born to an Australian and a Czech...if anything were to happem and we needed emergency evacuation to a country with better medical facilities, its impossible as the baby has no passport.....so we think its wiser to play it safe and have the bub in Oz.

Thanks in advance,

hinakos