We have traveled on some long trips to fairly remote places and we always carry a spare. I go a little further and take a jack with tools to remove a tire and a torque wrench to properly tighten the lug nuts after replacement. Have never had to use those items (other than a practice in the driveway). But feel so much more comfortable knowing if needed I can do it myself.
If you have a rear bumper you can get a spare carrier that will attach to it. If not then the they have carriers that attach to the receiver hitch.
Great time to plan your trip to Alaska. Cheap gas and USA dollar is strong. Probably reduce your overall costs by 30%.