It's not "private" its publicly owned.
If what has been previously posted is true, then is it is "owned" by the ratepayers of Gympie, not the Commonwealth. They have elected a council to manage their assets. The council has imposed conditions of use on behalf of the owners. Who are we to say they can't? You might not agree with them, but that's your problem, not theirs.
Public facilities are not for the use of citizens but rather on conditions dictated by the government
In almost all cases, yes. The government being what ever level of such that provides said "public" service. You can't borrow a library book with out being a member of the library, or at least registered with them in some way. You can't use the local "public" pool without agreeing to abide by the terms and conditions of entry. You can't drive
your car on a "public' road without it being registered, you being licensed to do so, obeying the road laws, and the vehicle itself being subject to an external assessment of whether it is fit to be on said "public" road (ie roadworthy). Public toilets have conditions of use, Public parks have conditions of use. Public car parks have conditions of use. Where do you think you actually have any free reign in a public place, while using a 'public' facility. What make you think a "public" aerodrome is any different?
Traffic,
I earnestly suggest you acquaint yourself with the rules about interfering with aircraft
In the Act, if the interference is done with lawful authority, then it's not unlawful interference. The terms of use would have to be quite specific in this case I suspect.