Twin2040,
We have just been through this process as we are planning to be down under next month.
Don't Worry is correct, private flights are not eligible for CTA.
CTA applicable for commercial/charter flights.
Furthermore, if you plan to do any internal flights (Private) then the ball game changes.
You will be required to get a Temporary Work (Short Stay Specialist) Visa Sublclass 400.
https://www.border.gov.au/Trav/Visa-1/400-
ADG