Planning move to Australia Next year. Needs some general question answered.

Hi, I am planning to move to Australia sometime next year on work VISA and I and my family(wife and one kid) have NZ permanent resident VISA. Can someone please answer following questions, so that I can decide whether it is the right move or not:

1. Will I get any medical benefit from AUS Govt. on Aussie work VISA?
2. Can I get free schooling for my Kid as I have in NZ? My son is just above 5 years old.
3. If my wife falls pregnant there in AUS, would I be eligible for any benefits or I need to pay all amount from my pocket until and unless I get AUS residence? Thanks, Syed