I got my HHII LS last April and all the tires looked good. I didn't get a spare so I bought one, then had a blowout. So I picked up another and had new tires on one axle. Good thing I picked up a spare. Trip last fall blew another, now have 4 new tires and a "good looking" spare. My HH has a 13,500 lbs gross.
I would check the date codes, if as you suspect it's a low mile rig the tires may be original. I would not chance Alaska on the original tires. 4 new ones on the ground and at least one mounted spare. You could carry another unmounted tire as a backup if it makes you feel better. Repair shops are few and very far between in the northwest. I wouldn't for see any problems with new tires but there's always the unexpected.