When I had DD I was in a shared room that could accomodate 4 but had it all to myself - is really just the luck of the draw. Unless it's been renovated in the last nearly 10 years though, the rooms and facilities are quite old and I probably wouldn't recommend it if you like your creature comforts. The staff and everyone were lovely though.

Having a Baby in WA has a lot of info on both public and private hospital options, you will generally find it's difficult to guarantee a private room in a public hospital unless you're being treated as a private patient and even that could be hit and miss. But then, same goes for private hospitals if they're having an extremely busy period - it's just the chances are higher and they make every effort to get you one.

FWIW, I'm booked in at SJOG Murdoch with Dr Mincham for this one - so far he's been completely awesome.