Hi Stephanie and welcome to BB.
Yep, the medicare system is complex - and going to your GP to get a new referral for a new condition or when your referral runs out has always bugged me - seems to just be a waste of money for the govt to be funding trips to the GP just for a referral. anyway enough of my whinging.

Public hospitals will vary with the "model of care" they offer for pregnancy eg. most have midwife only clinics where you see mainly widwives but see a doctor 3 or 4 times, usually again just when a referral is need for a test or u/s. some have homebirth clinics, some have where you see the same widwife all thru antenatal to postnatal. I think some have high risk clinics. Where do you live in Melbourne? I went to box hill hospital and they are good but check out your local public hospitals services. They usually have that detail on their websites.
charges will vary - most public hospitals will send you for test on site so there will be no charge but for ultrasounds sometimes they send you to a private ultrasound place and therefore there will be cost on top of what medicare gives you.
Then for inpatient stay - you can elect to be a public patient and get no choice of doctor and then all your hosptial charges will be covered. Or you can be a private patient in a public hospital if you want to choose your own doctor (but the docor has to practise there of course) then you will get bills from the doc. and I think also theatre fees and anaesthetist as well. If you don't realy have a preference for doctor then there is no point doing that.
Probably best to ask your gynae when you see them. good luck