If you only want to get a PPL you can get one issued on the basis of your current Australian License. It will only be valid while you Australian license is valid. YOu can not hold a CPL on this basis. The limitations and requirements are here:
https://www.law.cornell.edu/cfr/text/14/61.75
Details about the process of applying are here:
https://www.faa.gov/licenses_certifi..._verification/
Note that you need to fill out a form for CASA so that they will release the information to the FAA, details at the link above. You will need to do a flight review before using your new license. Most places that will rent you a plane in the USA are pretty pragmatic and can bundle this into the checkout to rent one. If you are proficient it wont take very long and dosent require a Nav but brush up on your ground reference maneuvers(they are not part of the AUS syllabus).
If you want a "full" FAA PPL you can use clause 61.41 so that all your training to date counts for meeting the aviation experience requirements.
https://www.law.cornell.edu/cfr/text/14/61.41
The requirements for the issue of a PPL are listed here:
https://www.law.cornell.edu/cfr/text/14/61.103
These are fairly straight forward but note that the experience requirements include:
3 hours of flight training with an authorized instructor in a single-engine airplane in preparation for the practical test, which must have been performed within the preceding 2 calendar months from the month of the test; and
So you will need to do some training locally in the USA even if you meet all of the other experience requirements if you go down this path.