The Australian Sex Discrimination Act holds Gender as a protected asset, and this was upheld in the recent case of 'Tickle vs Giggle' where the company Giggle was found to have discriminated against a Trans Woman, Ms Tickle. The centre of the case was focussed on the definition of Woman, but the court held that the terminology has taken a much broader meaning in recent years, and that Ms Tickle's gender had to be recognised.
In general, Australians are pretty laid back, and only a few radicals care about Trans people. Everyone else just lives and lets live. Most places are as safe for Trans people as for Cis people, recognising that there is crime in every society. I have travelled a lot around Australia as a not really passing trans woman and have never been harassed, but I have heard stories of Trans people being harassed at places where alcohol is consumed.
Having said that, we are weeks from a Federal Election, and if the conservatives won power, things could change, though it is not likely as the Conservative Party suffered a severe backlash at the last election for proposing anti trans laws.
Hugs,
Allie