We got all new tires before our Alaskan trip and ours were 6 years old. I would recommend you change yours out.
We went up from Arizona by way of Oregon and that's where we bought our tires - no sales tax which saves a lot. We preordered them and specified no older than 6m age on them. They all came in with a date of 3m. We got the Michilins from Les Schwaab in Coburg at a very good price after pricing them at other places in other states.
We had absolutely no problems with anything on our all-summer Alaskan trip. Have a good one....and be safe.