I just did the drive from yale michigan to wasilla ak 4300 miles last month took me bout 7 days mostly driving with some stops hear and there. From Montana it took me bout three days but one of the days i spent fixing my jeep. I would drive it you cannot beat the scenery on the Alaska highway. I would recommend reading my topic on the trip I updated it every day of the trip with lots of pictures and info.http://www.jeepforum.com/forum/f12/4000-mile-trip-yj-alaska-1083144/
1st tip make sure everything is in tip top shape you will not see auto parts stores for hundreds of miles trust me on that one You should not have a problem with your 2010 wrangler though.
2ed bring extra gas It saved my *** when i ran out before i reached whitehorse if you drive at night alot of gas stations are closed. And bring stp fuel treatment I ran into bad gas a few times.
3ed you will not have cell phone service in 90 percent of the time in northern canada some places they dont even have 911 service.
4th have a good set of off road lights if you drive at night lots of wildlife and sharp curves.
5th the road gets in really bad shape lots of dips and gravel sections in northern canada
6th enjoy the trip its a trip of a life time what part of Alaska are you going to?