Two great sources of information about the Australian economy are the Commonwealth Treasury and the
Reserve Bank of Australia(RBA). Most economic data for Australia is published by the Australian Bureau of Statistics(ABS). While the ABS charge for most of their data, they also have quite a bit of free information.
For an overview of current economic conditions in Australia I recommend the relevant chapters on the economy from the Budget papers which are usually released in May each year. If you are looking for economic information in November/December or before there has been a budget, there is usually a mid-year update as well.
2001-02 Budget (May 2001): economic summary : chapter on the economy
Mid-year update (November 2001)
The RBA web site contains a good set of charts of key economic variables which would be useful resource for students studying economics or non-economists who are interested in what is going on in the economy. The RBA also issues quarterly statements on monetary policy which typically include a comprehensive discussion of current economic conditions in Australia. It is also worth a look at the recent speeches made by RBA officials since these also frequently contain valuable insights and are more frequent than the formal statements mentioned above.
Please feel free to send me any comments/suggestions.