The registration process required aliens to submit a number of 'RA' (Registered Alien) documents. The range of forms to be completed included the following.
RA Information from Aliens over Sixteen Entering the Commonwealth
RA1 Application for Registration Form
RA2 Application for Registration by Alien Entering Australia
RA3 Notice of Change of Occupation or Employment
RA4 Notification of Departure from Australia
RA5 Notice of Change of Residence
RA6 Notification of Marriage
RA7 Notification of Naturalisation
RA9 Application for Issue of New Certificate
The most commonly used form was the Application for Registration by Alien Entering Australia (Form RA2), which in practice appears to have been issued for both resident aliens and aliens leaving the Commonwealth. The RA2 form varied slightly in format over time but recorded the same details about aliens entering Australia. These details included name, address, nationality, date and place of birth, occupation, place and dates of birth of spouse and children, name of ship or aircraft registration, date and place of arrival in Australia. A passport-sized photograph of the applicant was attached to the majority of forms.
You can now access these types of documents from the National Archives.