I made the trip twice - once to Fairbanks, and once on the way back a few years later. Both trips were in late summer (August/September). Alaska was an awesome experience.
I was solo on the way up in a pickup towing a utility trailer. I drove from Las Vegas to Fairbanks over 6 days, 12 hours of driving per day. I made around 600 miles most days, but the day I drove through Seattle, I only made it half that far - damn traffic! Total trip distance was about 3500 miles. The scenery was GORGEOUS, and the road was in pretty good shape. You're definitely in the middle of NOWHERE as you drive through northern BC and the Yukon Territory.
On the way back, I was with SWMBO and our small dog in an SUV, again hauling a small trailer. We took a pretty circuitous route to New Mexico, spanning about two weeks, visiting family along the way. We drove over 4,000 miles! The dog got used to life on the road pretty quickly, and we really had a great trip.
I know you've chosen not to drive, but here are some tips for anyone who wants to make the trip:
Get a GPS and bring a cell phone. As you get into the "wilderness," the cell phone will only work near some of the bigger towns, but it's better to have one than not.
Buy the annual publication, "The Milepost." It details nearly every mile of the ALCAN highway and several alternate routes, including gas stations, hotels, restaurants, attractions, and a bit of interesting history.
Bring about 10 gallons of gas in cans. You probably won't need it, but it'll give you peace of mind. When services start getting sparse, never pass an open gas station without filling up. Some towns only have one gas station, and if they aren't open for some reason, you'll be stranded. Be prepared for high gas prices in Canada.
DO NOT drive after about 9:00 PM in the more desolate areas. The deer/elk/buffalo threat is very high. Service stations often close after dark. Pay at the pump/24 hour service is NOT as common as you expect.
Don't bother bringing firearms unless it's an absolute necessity. Canada makes you register them ($50 fee, each, I think), regardless of how long your stay will be. Handguns are forbidden. If you're doing a military move, the military won't reimburse firearm registration fees.
Party with the Canadians...especially in the really small towns.
Settle in for a long haul, and enjoy the trip!