If you want to go private, the thing would be to research private hospitals and Obs. You might like to start with a list from your PHI provider - they have lists of who they deal with. BB is a good resource to research the kind of Ob you'd want (low intervention/breech/high-risk). Then you call for $$ details from Obs and hospitals (after checking what your PHI will cover you for).

e.g. my PHI will cover me for hospital (less $250 excess), including any surgery if needed. Some pathology may be covered, some not. The Ob is covered for in hospital. I think Obs also charge for "pregnancy maintenance", some of which you can get a rebate from Medicare - others can confirm this, never got that far. I'm not sure if anaethetics, including epidural are covered.

I like Flowerchild's idea of having them standing by if necessary, but not having them around otherwise - though it does mean paying for them to do not much. I'd definately have my own private midwife though (heard too many stories about the potluck of hospital midwives)

Some PHI's cover independent midwives