Australia is in an interesting position.
We have a Pentacostal PM on the one hand, who is making sure religions are free from discrimination law, and as part of that, is very anti gender ideology in schools. And look, to give these people their due, during the very antagonistic marriage equality debate we had here a few years back, one of the most raised issues with me - a Yes voter - was slippery slope issues re gender. Yes, we could do that (marraige) but here's what we worry is down the line. Well, they were right to be worried about the down the line business, not about the marriage stuff though.
I think that laws vary by state. Minors used to have to go to court to have treatment; that's been abolished, I think. My state is reasonably restrictive (under a conservative government for the last few years), other states are way more liberal (under labour governments).
I really don't know much about specifics. I do know that we have onerous anti-discrimination laws, which involve laws against offence. There's supposedly a second part to that law that protects genuine need for free speech but the exceptions are very limited.
People at all stages of transition are protected under our anti-discrimination laws due to their gender identity.
In my state, you can't change your legal gender without having gone through gender affirmation surgery.
Other states have removed this requirement, meaning it's self declared gender identity in those states.
Short answer - in AU it varies by state from very liberal laws (self ID) to rather restrictive (surgical requirements) - but all transgender people are protected from all forms of discrimination in public places, including online, on the basis of their gender IDENTITY.
Other Aussies, come and fix my mistakes here if I'm wrong. I am currently thankful we live in a more restrictive (conservative) state, even though I'm a Labor member and voter.