An Australian resident doing business in the US
If you want to pay tax in the US, the best way for a non-resident is typically to set up a US C-Corp and then have the C-Corp pay US tax on it's US earnings.
The owner will obviously want to take some of the earnings out of the corporation and that can be accomplished one of three ways:
1. as wages,
2. as consulting fees, or
3. as dividends.
Taxation to the individual owner of the C-Corp will depend on how the owner chooses to take money out and the nature of the services being provided by the owner to the corporation.
The individual is or is not taxed in the US by determining if the owner is performing those services as a income effectively connected to operating a business in the US or not. I can not speak towards Australian tax, but generally income that is taxed in the US is not then also taxed in Australia and vice versa.