Another one here thinking your trip is too short for the expense.
Also, I'd recommend not flying into Fairbanks but instead, fly into Anchorage as there's much more to see in the area of the Kenai Peninsula. Also, there are more rentals out of Anchorage.
The best though would be to drive your RV up there. Millions have done it and many go back for more. Hubby might be hearing tales of years ago. Nowadays the roads are paved. However, there will be areas of construction going on as there are in the lower 48, also. You just drive slow and you'll be just fine. 2-3 months is the usual time for the driving trip. There is so much to see before you even get to Alaska. We didn't get any damage on our motorhome or our car on the drive.