Having made the trip many times, and lived in Alaska for nearly 20 years, I don't think you'd have a problem. The first few trips I made in the 70's were on gravel roads, replete with broken axles and all the horror stories, like a huge rock being thrown through the windshield from a passing truck with dual rear wheels. Fortunately, the rock missed everyone in the car.
Today, the road is paved all the way, and high speed travel is without the perils of the past. Do watch out for frost heaves, however, where the road bed is broken during the severe winters. There are two basic routes - the Alaska Highway north from Montana, or the Cassiar Highway, north from British Columbia. The Alaska Highway is probably the easiest route - both are very scenic. The Cassiar was an old logging road, now upgraded and paved, although construction may still be underway in places. I've done both.
Timing is another issue. It can rain a lot along the way, and flooding can wash out the highway on occasion. I'd recommend July and August. By August the mosquitoes (a large swarm can easily pick up a Cobra and carry it away)
start dying out, and by July the road damage is normally repaired.
Realize that it's a LONG trip, and the roads in Alaska only go to Fairbanks and Anchorage. We moved from Homer, Alaska, to southwest Colorado, and the trip was 3745 miles.
Alaska is a BIG state, and it will take along time to see it. Plan on about 3 weeks, 2 at minimum - with 2 weeks, you'll get there just about in time to turn around and come back.
Get a copy of "The Milepost" - a mile-by-mile travelogue of the entire trip north, with gas/food/lodging information as well as historical sites of interest. Speaking of lodging, do NOT stay at the Toad River Lodge...
http://milepost.com/
Hope that helps....