If your not covered by medicare you'll end up having to pay to go to the public hospital to birth too, might be worth looking at the cost of birth centers, private midwife or home births as well.
I'm booked into the St Vincents private in the city (Melbourne) which I had to book early in the pregnancy but that doesn't help you with cost sorry
My SIL just had a baby in QLD and she's not an Aus citizen, she had to pay for the OB and her hospital birth/stay in a private hospital and It cost her about $5,000