my sister had a baby at a private hospital (Qld) she was allowed her husband and a choice of birthing support person. She ended up wanting mum to go with her but she was allowed to have a midwife or Doula if she wanted but only to assist her not the birth. They dont do share care though and she did have to have an Ob that was with that hospital, which meant a little calling around to all the hospitals that the Ob worked at to find which one had an availabilty.