We have been to Alaska 5 times, two by air and 3 driving.
The first two driving trips were in less than 40 days, while still working. Like you, we couldn't get any more vacation days off of work.
You will have to drive between 500 and 700 miles per day to get to the Alcan Hwy @ Dawson Creek. After that the ability to drive that far is limited by the road conditions and your desire to see the different things you want to stop and see.
When you get to Alaska you will probably want to have reservations at the spots that are important to you.
Both times we either drove the motorhome to our place of interest or rented a car to get there. Most attractions are RV friendly.
If you know someone that has driven to Alaska, ask them lots of questions about their trip and what they saw and did while there.
We did the "circle" with the Kenai Peninsula and Valdez legs. Tok,Fairbanks,Anchorage, Homer,Seward, Anchorage,Glenallen, Valdez, Tok, and head for home. We did not see everything these trips, but we hit the "high" spots that we wanted to see.
Buy an up to date Milepost and spend some time looking to see what you want to see and do. Keep in mind that most of the reviews are written by the business owners.
The most important thing, HAVE A GREAT ADVENTURE!!!
Good Luck,
Journey Indiana