I too am from Brisbane and I've heard that certain private hospitals are booked solid with 30-40 people a month on waiting lists to get in. So I would recommend researching ahead of getting a BFP so you know where you would like to go, that way as soon as you are pg you can ring and book.
I rang the hospital I wanted to go to (from hearing advice from friends and family who had delivered there) and asked for a list of ob's who deliver there. I then picked one I had heard of and who a friend also recommended to me and my GP knew of. I booked the hospital the same day I saw my dr for a positive BFP. I booked the ob first though because until someone agrees to take you on, you can't book the hospital.
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