Whitestuff, pretty sure you can't do that! Going into private hospital, you would have had to under the care of a visiting obstetrician.
Private really ensures you have the care of one ob over the course of your pregnancy. Of course, there is always the possibility of the ob being rostered off if your wife has the baby out of hours or during their holidays, however, the ob usually will let you know who will be the replacement. My ob works in a practice with 2 other obs, and they take it in turns to do weekends. I have the option of meeting them prior to the birth.
Check with your PHI what their coverage is like for the hospital you are booked into. i had no OOP for my hospital as it was "partnered" with my health fund. I also had only about $200 OOP for my anaesthetist who gave me my epidural. Remember that you may have a co payment or such to pay for nights in hospital. My PHI will need me to pay $250 per night, up to a total of $500 for my hospital stay. ($500 is the maximum I pay for my membership year though, so although I stay 4 nights, I am only having to pay 2). The money you pay at Obs appts will go towards your safety net. Once you reach about 2000 I think (probably wrong, but info is on medicare site), you get a substantially better rebate. Trips to your GP etc add to this safety net, so it is worth making sure you are registered as a family - just call medicare.
Note also that if this is your first baby, you will need to check out your cover and find out when your wife will need to change cover to a family insurance. Usually it is about 10 weeks prior to the birth of baby. If you had twins, and weren't covered, then twin A is covered, but you need to pay for twin B. If you have a singleton, usually all is fine, however, if your bub needs to go into NICU, they need to be insured or else you will need to pay costs for their stay, which can be substantial. Note that once you have family cover, all children thereafter are covered.
Public means you have different options. You also will find that your care is covered under medicare. You have an option of shared care - where your wife has care shared between her GP and the Ob at the public hospital, or there is a midwife birthing suite, where the care is taken out only by midwives, but your wife must be in tip top shape and the pregnancy be progressing with no problems for this. You can also choose to have ob only care. The main difference is that with public hospital, you have no choice over the doctor you have. Each appointment can be a different doctor, and this can sometimes play havoc with continuity of care. HOWEVER, if there are no problems with the pregnancy, this is often a great way to go and no different opinions of care between the docs will arise.
You can choose to go private in a public hospital, however, you will still pay for your obs fees, and this usually will just mean you don't have much OOP for hospital stay.
Note, that the obstetricians who work in public also work in private, so you aren't necessarily missing out on quality of care. Going public doesn't mean that at all, however you lose the choice of doctor option.
HTH - hope it makes sense too!
Personally we are going private. I like being under one obstetrician, and I like the way she delivers care. I have a great rapport with her. I like that she knows any issues I have had previously and I don't have t go through the story every time I see her. I also trust her implicitly.
Note also, if you choose to go public, that you have the right to a second opinion if you do not agree with info that a doctor has said to you, or you are not so sure of their decision.
Good luck for you and your wife.