You might make it from Virginia to Tok in 11-12 days. We have driven three times from Maryland to Alaska, but have never driven straight through without stopping for a day of rest here and there along the way. We usually spend two nights in Whitehorse as it is a good place to stock up on food and take care of any issues with car/truck/motorhome. Also if you are driving the Alaska Highway there are places along there where you will want to take time to stop. We have taken 9 weeks twice to do the trip and 12 weeks once. Our 9 week trip this year did include Oregon and Washington, but we also did not go to several places in Alaska that we have already visited several times. Taking only 30-40 days to travel to and from Virginia to Alaska is really making for long driving days and very little sight-seeing.
We spent almost 4 weeks just in Alaska this time and spent no time in Fairbanks or Anchorage, just overnight stops.
With only that little time, you might do better to fly to Anchorage and rent a motorhome and spent the whole time in Alaska.