I went private and knew which hospital and OB I wanted (recommended by a close friend) so I booked the OB as soon as I got my BFP (4 weeks!). I had bloods done by my GP twice to check my HCG levels but only because I requested them. When I spoke to the receptionist at my OB's office, she gave me all the info I needed at that point in time and booked in our first appointment with the OB which was also our first scan - at 10 weeks. My OB doesn't generally do appointments any earlier due to the chances of miscarriages. At that 10 week appointment, our OB told us everything else we needed to know (again, at that point in time), filled out the referral to get our 12 week scans done and we asked some questions.
HTH