The question of ASIC requirements for crews of foreign aircraft not engaged in international RPT or charter ops is a question that still has the OTS scratching their heads.
ATSR 3.05 Crew of foreign and state aircraft etc
Despite regulation 3.03, the following people need not display
an ASIC in a secure area:
(a) a person who is a member of the crew of a foreign aircraft
(other than a state aircraft) that is engaged in a regular
public transport operation or a charter operation and who:
(i) is in the uniform of the aircraft operator; and
(ii) displays appropriate identification issued or
authorised by the aircraft operator;
I have seen a guy with a european registered Piper Cheyenne entering and flying around Oz but depending upon the airport operator, it can create some headaches. Tonym3's advice below about being escorted is probably workable as getting the ASIC prior to arrival would be problematic too. Perhaps you could arrange through Aviation ID Australia to have an ASIC applied for and ready for you on arrival at your point of entry. This can be done but just takes a bit of coordination with regard to the visa checking requirements. Not impossible though.