Your driving days (GOING TO Whitehorse) can be long (whatever you are comfortable with) but I strongly recommend you take advantage of the various stops along the Alaskan Highway and be a tourist where possible since you may not return on this same route. Many RVers go up on the Alaskan Highway and return on the Cassiar Highway (down through the middle of British Columbia). Coming back south on the Cassiar Highway also gives you the opportunity to stop at Stewart/Hyder—two towns sort of married together, one in Canada and one in the USA, on the coast. Depending on the time of year (of course), there is great bear-watching in Hyder.
Until you get to Fairbanks, I recommend boondocking as much as possible because many campgrounds are not worth the effort it takes to pull in. Some charge a lot for almost nothing, they are somewhat spread out, and not too plentiful. There are tons of boondocking sites. Some Canadian campgrounds that far north have 30 amp but many just 20 amp, some NO power, some with no sewer anywhere, and well water that will choke a filter, you are parked on dirt, if it rains you are in an instant sloppy mess, and driving lanes through the campground will be heavily treed with limbs automatically brushing the dirt off your coach. My choice is to NOT use them unless we have to dump and take on water.
Getting up there (and back) is much more demanding than running around in Alaska.