According to the CASA website:
As a general rule, pilots seeking to convert a foreign licence to an Australian flight crew licence must:
Pass a conversion exam, which for:
- PPL aeroplane & helicopter currently consists of Flight rules and procedures and Air Law (PAOS or PHOS) written exams and a flight test.
- CPL aeroplane & helicopter currently consists of Flight Rules and Procedures (CLWA or CLWH) and Human Factors (CHUF) written exams and a flight test.
- ATPL aeroplane & helicopter currently consists of CPL Flight Rules and Procedures (CLWA or CLWH) to be passed first, then ATPL Air Law (AALW) and ATPL Human Factors (AHUF) written examination/s. In addition, for conversion of an overseas ATPL(Aeroplane), the command instrument rating examination (IREX) shall also be passed.
- Obtain an Australian medical certificate.
- Possess or pass an ICAO required (oral) English language proficiency (ELP) assessment. CASA has sole prerogative to determine which overseas ELP to accept. A minimum of ELP level 4 is required.
If you just want to fly privately there is a Special Pilot's Licence.
More info here on obtaining an Australian licence - Civil Aviation Safety Authority - Converting foreign licences