I would check out some of the expat forums, as even though it is on the SOL, lots struggling to find work. The SOL is a little mickey mouse, lots of professions that really should be removed as some of the professions listed do not have enough roles to be filled. You would really do a lot of homework on this as can take years depending on the route you want to take.
pomsinoz.com
expatforums.com
What type of visa are you looking at Working Holiday or going for PR and looking to relocate permanently?
Best bet get into a Multi National, work a few years and see if they would relocate you. This is by far the easiest and cheapest option!
As for Sydney, I would avoid unless you are making a very good 6 figure salary. Melbourne, even though not as expensive is a much nicer city.
As WildColonialGirl pointed out this is a fairly slow board outside of NA.
Have a look at
www.domain.com.au to get an idea of rental prices. If you are coming from NY or SF, you will not be as shocked.
forums.whirlpool.net.au is a very active Australian forum and you can ask about the job market for accountant roles.
As you are looking to move from the US, suspect you will find the cost of living a little different here...
Would you be looking to move here and try to find a job or after you hopefully get a visa, see if you can find an employer to hire you before you land. The latter will be very difficult.
Have you considered the relocation costs ie, visa, flights, temp accommodation, rental deposit(bond), 1st months rent(if you do not have a job they might want 6 months rent up front), freight shipping, money to cover you if you cannot find a job quickly?
This could equate to anything from $20000 and upwards.