That should be a very nice trip, not sure about the move, lol, a little cold that far north for me
Take Flat repair stuff, air pump, extra fan belts, coolant and oil; duct tape and bailing wire
Just a heads up about Canadian boarder, have Passports or "enhanced drivers license", for everyone.
Since I assume you will have some home stuff with you, they will give you the once over since they may think you are trying to move to Canada illegally, if you have emails or other documents providing a reason for the move to Alaska, print them to show the officers.
If you have pets they/you need proof of vaccinations.
You can bring long guns but need documentation, NO hand guns are allowed, ship it UPS.
If you have ever been convicted of a criminal offense they can refuse entry, DUI conviction is almost an automatic refusal, no matter how long ago it happened, but you can get a travel permit(ministers permit) ahead of time, this can take a few months, and a few $$.
If you lie about anything and get caught at it, you will be taking the auto ferry to Alaska.
Bellingham, Washington(20min south of the border) to Alaska auto ferries sail every Friday year-round, 1 truck with 2 people(1 cabin) runs about $4,000, takes about 5 days.
I am just speaking from what I think is correct, call Canadian border services and talk to them for exact info on doing a transit thru Canada, I would hate for you to get stuck at the border, Canada is a nice place, but Border Guards can be anal about the rules, that goes for US border guards as well.