From the Australian Government ASIC Website:
What is an ASIC?
An Aviation Security Identification Card, known as an ASIC, is an identification card which is used to identify a person who has been the subject of a background check.
An ASIC is required to obtain unescorted access to the secure areas of security controlled airports that have regular public transport (RPT) services.
Reading this, I can't see a requirement to have an ASIC, additional to my current company card!
My company card is issued by one of the Issuing Bodies!
Whether I am flying commercially or privately is not relevant! I would expect it to be accepted Australia wide regardless!