Should I replace my TRUCK tires before Alaska trip?

I will echo the others replace the tires.
Trailer tires and flats, new or old the biggest problem is under inflating the tires.
Maintain proper inflation for the load you are carrying.
When rplacing the tires have a true weight of the vehicle/trailer LOADED before you buy the tires, then buy tires capable of carrying that capacity.
The tires that come on most trailers are usually under rated as are the axles.
Make sure you pull the hubs grease the bearings before heading out you should be fine.