I'd just like to point out for those who are following this thread and aren't Aussie, Tasmania is actually a beautiful place, and lovely to live in. It makes me think of Scotland with the green countryside and colder weather!

For some reason the rest of Aus picks on Tasmania, and I've never been able to work out why; I visited once and never wanted to leave again!

I couldn't live there myself though; their quarantine laws are ridiculous, and my fishkeeping hobby demands I have access to outside sources! -goes off on random tangent-
Anyway! As others have said, the treatment here can sway from one extreme to the other; it took me close to two years to get on hormones because I had no help, and none of the people I went to wanted to put me on T, Yet others I've spoken to have been put on hormones within the first few weeks. It really does depend on who you go to, which state you're in, and factors like how old you are.
Some interesting Aussie tidbits that might help sway you (though I don't know how many of these will help immigrants):
1). Our licences don't have a gender on them.
2). It is possible to change your gender on records before having surgery or going on hormones.
3). Top surgery will be partially covered by Medicare regardless of your legal gender at the time of surgery (with further coverage available through private).
4). Hysto/oopho will be partially covered by Medicare if you are legally female (with further coverage available through private).
5). A legal name change takes around a week to process, and will cost just over $100.
A quick breakdown of our anti-discrimination laws by state/territory:
NSW: 'Transgender' covered in anti-discrimination laws since 1977.
ACT: 'Transsexuality' covered in anti-discrimination laws since 1991.
QLD: 'Gender identity' covered in anti-discrimination laws since 1991
SA: 'Chosen gender' covered in anti-discrimination laws since 1984.
VIC: 'Gender identity' covered in anti-discrimination laws since 1995.
WA: 'Gender history' covered in anti-discrimination laws since 1984.
Neither TAS or NT cover transgender people in their anti-discrimination laws, though it could be argued that a transgender individual's status falls under 'irrelevant medical history' (which is covered in both) in certain cases.
Australia's six most expensive cities ranked as of Mercer's 2011 Cost of Living survey:
Sydney - Globally ranked 14
Melbourne - Globally ranked 21
Perth - Globally ranked 30
Brisbane - Globally ranked 31
Canberra - Globally ranked 34
Adelaide - Globally ranked 46
It's worth noting that the Mercer survey compares against New York, and as such is skewed to an American market. One also has to take into consideration that the average Australian earns (as far as I can tell) more than the average Brit or (I assume) American. For example an English cousin is staying with us at the moment, and we've worked out that her salary as a full time (40+ hours) nurse converts to around $35000 Australian. To put that into perspective, my annual income as a part time (20+ hours) assistant manager in a retail store is $39000 (and let me assure you that is at the bottom end of the Aussie pay scale). So while the cost of living can seem high here just from looking at the numbers, from what I can see the average wage is more than capable of coping, so don't let that scare you off!

I hope that's been of some help!