You're going to be fine piece of cake IMO. I've hunted in Hawaii, basically live in Wisconsin every November & I've hunted elk in Utah. Utah is a really gun friendly state. The guys above have it right. Make sure your weapon is unloaded,
take your bolt out of your gun if it’s a rifle. They will ask to see the firearm. Sign the firearm declaration. I've always flown with my ammo in locked in my case with my gun. I usually fly Delta, American or South West. I try not to fly on United with a gun because they have a hub in New Jersey and I've heard some horror stories about United & guns. Make sure you have TSA approved locks. And yeah they'll probably do an explosive power swipe of your hands.