Before delving into the cost of food, housing, etc.. one should firstly ascertain the amount of disposable income one has.
Unless you are moving from America, Japan or similarly high-tax country I suggest that you do this key bit of analysis. Because, even if “things” are cheaper per se in Australia it means jack if your disposable income is cut in half by coming here.
You’ll need to firstly figure out what your gross income will be in Australia. If you’ve got a job offer to come here then congratulations, that bit will be easy to find out.
Otherwise I would use the rough rule of thumb, whatever your salary is in USD, convert that into the same nominal amount in AUD. I.e. if you were in HK and earning USD100,000 p.a. you’d probably get AUD100,000 p.a. here. Your milage may vary, suggest you get professional advice, e.g. speak to headhunters and ask what someone of your caliber would earn here.
Next is to figure out the tax you’ll be paying. You should already know what your effective tax rate is in your current jurisdiction. Go to the ATO (Australian Tax Office) website and figure out what your new effective tax rate would be.
In Australia, the mandatory pension fund is called superannuation or super for short. You have a choice of which fund your employer funded mandatory contribution go to but you have to elect a fund. This is typically 9% of your pay. You need to find out whether the gross salary quote in  above includes this amount or whether your employer will pay your contributions on top of your gross salary, usually it’s the former 😦 .
GST (goods and services tax or value-added tax)
In Australia there’s 10% GST on almost everything so if you come from a country with a lower (or no) GST then your effective disposable income has reduced by the amount you purchase each month!
If you aren’t a citizen or permanent resident then you’ll have to fork out for an expensive visitors health policy. If you are “permanent” then you have the option of which private health care you take out which is cheaper than the visitors health policy but still you’ll need to budget for it which would be a shock especially if you come from somewhere like Singapore where people typically take out critical illnesses but not health insurance.
Hope that helps in your first step in determining the cost of living in Australia for you, which is to figure out the pot of money you’ll have to play with each month.
I’ll go into Accommodation, Food, Transport in a later article(s).