From a good friend in Australia, who is a mother of eight - and has been through this issue as a child and a mother:
Off the top of my head:
* Victoria is the only state where H/S is permitted without any requirement to seek permission or declare it. i.e. Freedom to H/S as one pleases.
* Western Australia allows it, provided each child is registered (small annual fee) but the State monitors the curriculum and progress etc of each child. The State can also refuse to approve registration, then one is forced to enroll children in approved school within short time-frame. Many H/S ers don't register and therefore can teach their own curricula (and are breaking the law but often get away with it). Some have been "caught out."
have been fined, forced to register and conform to State-approved curriculum.
* South Australia has slightly tighter H/S laws than WA.
* Queensland and New South Wales are similar to WA.
* Not sure of Tasmanian nor Northern Territory laws, other than they don't have total freedom as has Vic.
I'll do a Google Australia search and see if I can send you some links with more info.