Hi Eva,
To be honest...... I don't know of anything like the Englishforum in Australia because Australians generally like to talk (unlike the Swiss), and you won't have to look too far to find someone that could help you (government departments excepted).
Another thing, Where exactly will your family be moving to in Australia?
This would largely influence any advice someone could give you.
Public transport in Australia is terrible by the way.
Trains and busses are only "OK" in the major cities, and yes as the previous poster mentioned, it's cheaper to fly between the major cities than to drive (Perth to Sydney is a flight between 4-5hrs, East cost cities are between 1-2hrs).
ALL public transport timetables are a work of fiction, so I'd save yourself the hastle looking for that information.
Unlike Switzerland, you will need to consider getting a car at some point.
For a car purchase, I'd recommend doing your research on:
www.carsales.com.au
in conjunction with:
www.redbook.com.au
Carsales have excellent filters to sort out a car that you maybe looking for, while Redbook will help you identify what the original purchase price and trade in values for the car you are looking at.
Government websites are all excellent in Australia.... it's just the staff that are annoying.
Using GOOGLE will be enough to help you track down anything you need to know.
Real Estate:
Renting etc. these are the top two websites for renting and buying:
www.realestate.com.au
and
www.domain.com.au
both websites are super easy to use. You can't go wrong.
As I mentioned at the start, the best thing you could do is get involved with your community, and unless you intend to live somewhere dodgey, say "G'Day" to your neighbours.
People open up to you a lot more there than here so any questions you may have will make for an excellent conversation starter.