So, I have a Pty Ltd company, of which I am the sole director/employee (you can start one of these for a few hundred AUD, and it can all be done online).

For each US client, I fill out and sign a W-8BEN-E form (https://www.irs.gov/pub/irs-pdf/fw8bene.pdf) which means I don't need a US SSN and the client does not need to withhold any tax from my payments.

Each month, I then bill my US clients for hours worked, which they pay in USD via a foreign exchange broker (I use OFX), which then converts the USD to AUD and deposits it in my company's Australian bank account (this works out much better than an international bank transfer as the exchange rates offered by the broker are far better, and can result in a difference of a few hundred AUD a month).

This AUD gets lodged as income for the company.

Although the company is registered for GST, because the work is for overseas clients, I don't need to charge or collect GST from them.

I then pay myself a salary in AUD, plus the appropriate amount of super. The company deducts the appropriate amount of Australian PAYG tax based on that salary, which is sent to the ATO once a quarter.

The company is then taxed on any profit it makes - but that's typically low/none, because the salary paid to me is an expense for the business, and I can control the amount I get paid so I make sure that income - expenses = 0.