SB,
I didn't spend a lot of time and gave you some half answers...sorry. You can legally take a rifle or shotgun through Canada but will have to pay their fee to do so. I drove up on the ALCAN and back as well and saw no need to bring along a firearm. That said, however, we slept in motels and not out in the elements. I only lived in Alaska for two years and am no Sourdough or even a marginal authority on anything other than putting my socks on before my shoes.
My buddy bought his double rifle for around $8K and there are other, less expensive, options available. Daveinthebush, who will likely post again as soon as he gets back to Alaska from a trip to New York, carries a 12ga shotgun when bowhunting. I carried a 338 Win Mag rifle (with quick release scope mounts) or Freedom Arms 454 pistol when off the paved road in Alaska -- saw a few Brownies and lots of Blackies but never got too close unless I was chasin' 'em. I selected the 338 because I wanted a "do everything rifle" in Alaska. If the only mission was protection myself from toothy critters, I'd have likely chosen a 375 or something larger. As it was, the 338 was pleasant to practice with and accounted for a black bear, moose, and a couple of blacktail deer during my short tenure.
If you're a hunter, and think you might end up in Alaska in September, let me know. There are some easy to access areas for black bear.
Cheers,
Matt
P.S.
If you're even thinking about driving up to Alaska buy a copy of "Mileposts." There's not a better publication to lay out the ALCAN -- where to sleep, eat, gas, etc...