Each state you mention may require a different firearms licence. Our normal residents firearms licences are usually recognised by other states, but check that "visitors permits" are recognised interstate, as its very ambiguous. Most states require a genuine reason to issue a visitors permit, this is usually in the form of participation in a recognised clubs activity (recognised club hunts are usually fine), or a "promise of business" letter to a recognised licensed hunting guide. Licensed hunting guides are allowed to assist with your application in most states, but they usually must have a "promise of business".
Bringing a firearm in & out is several other sets of paper work & most overseas visitors borrow a rifle when here particularly if traveling to several states as we don't have a national registry. Firearms are state law & each has very different sets of requirements & the wheels turn slowly as they are badly underfunded/staffed & most still work on the old "XP ?" system.
Allow plenty of time, consider if its worth bringing your own firearms, but do get visitors firearms permits for the states you are traveling too. It's not worth the risk to use a firearm here without one.
IMO NSW is the worst state to get a visitors permit & to import a firearm if anyone is considering this state. We have a working group at parliament ATM, looking at the regs with the view to encouraging tourism, by streamlining the visitors permits if shooting under the supervision of a licensed hunting guide or firearms instructor. This isn't going to bring any relief in the short term though.
Good Luck
Sharkey