hi I was checking out this as we were planning our next baby before going to Australia and depending on when we got the Visa back we could have been traveling when i was pregnant. but your wife could attend a public hospital from the information i got back they are very well run and just as good as private ones if you check out a web site called Bellybelly .au.com they have lots of information on the hospitals and the girls there are very nice and be only to happy to help. i think as soon as you land in Australia you can get Medicare check out the Australian web site they have all the info on that.
Hope that has helped Good luck