Cairns and Brisbane.
Possibly Townsville and Gold Coast (Coolangatta).
Maybe Sunshine Coast (Maroochydore).
I'd phone those 5 airports and find out what's possible.
There maybe other airports available by prior arrangement. i.e. Most QLD maritime Ports have Customs and Quarantine who may be able to cover the airport at your cost.
Department of Immigration and Border Protection
If you are a Biz Jet operator, wouldn't your 'Handling Agent' be able to get that info?