Back around 12 or so years ago my son ( who was 12 or 13 ) and I spent a month driving from our home in Washington State, up central B.C., ( not the al-can highway ), up the Cassier Highway ( western-most of the N/S highways ), up into Yukon, Alaska, up to Prudoe Bay, and back down, going a slightly different way back. I had an old '68 Chev. Van, but heavy duty ( ex phone-co van ). We slept on a platform in back, with our supplies below it on the floor, and a canoe on roof-rack.
Once you get into Northern B.C., settlements have Laundramats, and most of those have pay-showers available. We only spent one night in a camp-ground, and I regret doing that. We would just drive off the road, and stay were we wanted ( discouraged now, but still being done ). We did some cooking, but also ate at "joints" along the way. DId some fishing, tried to do some black-bear hunting, but no luck. No problems of any kind. We did take extra belts for engine, radiator hoses, and a couple of spares, also some "flat-fixer" cans..didn't need any of it. We started in July, and saw a ton of bears along the Cassier Highway ( we only hunted in Alaska ). We took rifles with us, just declared them at Canadian Customs. NO HANDGUNS, of course, then, or now !!
I haven't heard about renting a car with the "survival equipment" ( including shotgun ), but I suppose if a car is rented up north, it likely has the essentials.
One neat way to consider, it to drive one way, then take the Alaska Marine Highway the other ( Ferry Boat ). You can rent rooms, or sleep on the deck.
One of the first things you should do, if you haven't already, is get a copy of the "Milepost", a guide to driving through B..C., Yukon, and Alaska. MUCH info in it, and if you go, take it with you, lots and lots of interesting stuff in it.
Enjoy,
Mark
feel free to pm if you have any questions I might be able to help you with.