If you don't have explosives, weapons or drugs, then yes, it is perfectly ok to take your consumer grade gimbal on a domestic Australian flight.
Airport security gets tighter every time there is a disaster and rarely loosens afterwards. I guess it's a good thing for our general safety, but it does become a nuisance when you have to throw away your brand new pair of toenail clippers every time you fly.
The biggest concern CASA has are batteries. Powerful modern li-ion batteries in particular. Most batteries for consumer grade gimbals are perfectly fine, like the G4 Plus, G4S, Summon and event the MG. Its when you get to the batteries that power items like power tools, drones and electric wheel chairs when you need to start to look at CASA's rulebook, I definitely recommend you read it before you head over to the airport. Or if you have time before checking in, just ask the least grumpy looking airport security officer.
We took our Feiyu G4S through Melbourne's airport security without a hitch. So bring your gimbal along, take some shots inside the airport, on the plane, just watch out for customs and the security guys, they strangely don't like being filmed.