The United States CDC has rescinded the Order requiring a negative pre-departure COVID-19 test result (or documentation of recovery) for all airline passengers arriving in the United States from any country.
The rescission is now in effect, meaning a traveller from Australia or any other country will be able to board a flight to the US without requiring a pre-departure Covid test. Australia rescinded its pre-arrival test requirement in April 2022. Travel from Australia to the US and back will now be free of any testing requirement, removing a significant hassle, risk, and cost from the process.
It is important to note that the US still requires foreign nationals (nonimmigrants) entering the US to show proof of vaccination against COVID-19 before boarding a flight to the US. The vaccination requirement has not changed at time of writing.