Just adding my 2 cents from Sydney, moved here when i was 17 weeks pregnant..
Medicare is definitely a must like the others say, near where i live i went to a bulk billing doctor so i had my appointments with him free of charge. He referred me straight to the hospital though which i prefer and with medicare thats free as well. The hospital women's clinic has both midwives and doctors who you see at various stages of your pregnancy and all appointments are in the same place.
I had my 12 week scan in NZ and was worried about the cost over here cos i had heard it can cost a lot but i had my 19 week one done at the hospital Free!
I haven't yet had my baby but as far as i know the birth will be free too. My whole maternity care here in Sydney has been free pretty much, as long as you are happy to go public which i am

- the biggest problem i have had is the waiting time at appointments, my last one i had to wait over an hour to be seen! So i now take a book, snack and water to keep me occupied.
I did have to pay for antenatal classes though which i guess are optional, at $150 for the whole course.