The company Leadie is referring to I think is Aviation ID Australia and yes they are very helpful.
What is easier than trying to figure out what is and what isn't acceptable as a tertiary ID document is an Oz drivers licence (if you have one). Unfortunately overseas ASIC applicants got screwed by the regulations.
Out of interest, does your NZ pilot licence have a photo? If it does, then that is a secondary ID like the drivers licence.