Travelling anywhere internationally with firearms is not easy but not impossible either. Given your LOP requirements you need to bring in your firearms to enjoy your hunt. You don't say what you're hunting or where you will be hunting, as different states have varying requirements. As long as you aren't going to or travelling through WA it shouldn't be too much of a problem bringing your firearm/s with you, assuming they are not semi autos or handguns. However you do have to apply for permits and I assume you will need a permit to take them with you outside of the USA.
From a previous post of yours it sounds like you're looking to hunt buffalo in the NT. Most likely you will fly into the East Coast, probably Sydney, and then take internal flights to your destination in the NT.
Any decent outfitter you use can or should help you with the process and would likely do or at least help with most of the paperwork required.
Good luck. It is a hassle but the trip will be worth it.
