??? The site says you're in Kansas, which is in the United States. Alaska is also in the United States and has been since 1959. You don't need a passport.
Unless you put the thing on a boat to get it back to the lower 48 I think you will have to drive the car through Canada at some point? You could drive it across the North Pole but I think Russia requires passports too.
You're making assumptions that I did not make. To just go look at the car, a passport is not needed. As far as getting it back to the U.S., given its condition and age, it would be foolish to drive that car the 2500 miles down the Alaska Highway to the U.S. It would not be a good idea to try to trailer it all that way, either. If anyone really wanted to bring that car to the U.S., the best and safest way is to have it shipped, in which case passports and so forth are the responsibility of the shipper.
If I had it shipped it would be the shippers responsibility. If the mechanicals are in great shape I'd risk driving it. Just take it easy and you should run less risk of major malfunctions. Be a great story to tell my kids and to tell at shows. Plus how often does one get to see the great U.S. and Canada scenery. That would worth most of the trouble I think. Just my opinion.