Due to the large size of the country, you must become a Private Investigator in Australia by becoming licensed in the individual states you are a resident of. To become a Private Investigator throughout Australia, you must obtain a PI license in each state. This is easier than you think. Once you become a Private Investigator in Australia and obtain one full Private Investigator license in one state, you can use that license to obtain other state PI licenses and circumvent each state's PI licensing requirements.
Australia Private Investigator licensing requirements by state: