hello
if you are a US citizen, you will have to pay US income tax on the income you generate worldwide - this holds also if you are not a US resident, only citizen
When you declare your income in AUS to IRS, and depending on the USA-AUS tax treaty if any, typically you may consider foreign taxes paid as a tax credit
a bit delicate, in particular if there are tax treaties in effect - a "trick" would be to have a professional specializing in this type of situation do your first return - you will then be able to mimic the future ones!