Australian Government - Attorney General's Department (AGs)
The AGs is responsible for registering all Marriage Celebrants through out Australia.
As a registered Marriage Celebrant they can legally marry couples and register their marriage exactly the same as any state run Marriage Registry Office.
Check on their site (below) to see if your Celebrant is registered.
To do this just type in their surname.
Example. Is Michael Teulon a registered Marriage Celebrant?
Just type in "Teulon"