I had DS2 at the public hospital, thru the birth centre (cmp) and in early pregnancy went they the early pregnancy unit (due to a previous ectopic pregnancy). I couldn't fault them, though be prepared to wait, which I think is standard for all appointments anywhere really.
The birth suites are brand new (my son was born in October and the new ward haven't been opened yet).
I attended my best friends birth directly thru the hospital and they were amazing, she had a fantastic midwife.
Like I said, you do spend sometime in waiting rooms (but then I did that going private with DS1 too) and you don't get to pick your doctors but overall I couldn't fault the care, though I transferred to cmp from my 22 week appointment onward.
I didn't stay in the maternity ward, there are no single rooms and I know some friends who got unpleasant neighbours and others who didn't have any issues.
I would call the hospital and ask what's best re: referrals but I would say they are going to tell you to get your current GP to fax they a referral. I believe they see you at around 10 weeks for your first appt (as I went thru the early pregnancy unit I seem them from very early - like 5 weeks early!).
Also unless you pay to go private, or have a home birth your only other option is the public hospital, through the public you can then go on the list for the birth centre (cmp). The bc is very sought after, and they accept 30 ( I think!) pregnancies per month. At one if your initial appts at the hospital they will discuss the bc with you and if that's the model of care you would like.