From the little I know the Australian medical is an ICAO medial, the FAA is not.
I don’t think you can validate an Australian medical to gain privileges above a private certificate. This is the link to
U.S. Pilot Certificates Issued on the Basis of Foreign Pilot Certificates Per FAR 61.75
Many doctors in Australia can do both FAA and CASA medical, sus one of them out and get both done at the same time. This is the link to
FEDERAL AVIATION ADMINISTRATION OFFICE OF AVIATION MEDICINE CIVIL AEROMEDICAL INSTITUTE AVIATION MEDICAL EXAMINER SEARCH
