According to the CIA World Factbook, America's GDP per capita - a crude measure of average national wealth per person - was US$43,800. According to recent figures released in June by the Australian Bureau of Statistics (5206.0 Australian National Accounts: National Income, Expenditure and Product. Page 23) Australia's GDP per capita is now AUD$50,440. When converted to US Dollars (US$0.9262 = AUD$1.00), this means that Australia's GDP is now equivalent to approximately US$46,720.
I don't have any stats on recent figures to work out what US GDP per Capita is currently, and anyone who knows about this area of economic comparison knows the shortcomings of such measurements. Nevertheless, you could argue fairly solidly that the two nations have now reached parity in terms of GDP per Capita.
This, of course, has very little to do with the wonderful strength of the Australian economy, but with the falling US Dollar. Almost every single nation around the world has had their GDP per capita income increased in relation to the US.
In other words, America is getting poorer.