The miles you make a day are very much tied to you personally. Ask yourself how many miles you normally travel when in the lower 48, 250, 350, 500, etc? You won't find it much more difficult to make the same mileage on the way to Fairbanks, IMHO. I am an early riser, often on the road by 7 AM or earlier and with photo stops or casting a line here and there, I can stop by 5 PM and still make 400 to 500 miles a day when driving.
So 4 or 5 driving days on the highway, plus stops, and a day from Jasper to Dawson Creek would get me to Fairbanks with no problems. Throw in a day for Liard River Hot Springs, three days for Whitehorse, perhaps a day to go to Skagway or a couple to go to Atlin out of Whitehorse.
This late in the season I can't imagine you having any problems getting a site at Denali NP to view Mt. McKinley. But if a reservation seems in order then make one. Some of our forum members like to only drive a few hours a day and set around the campgrounds the rest of it. Age, health, stamina all play a personal role in deciding your comfort level for driving, anywhere, not just on a trip to/from Alaska. I tend to go to Alaska and northern Canada to spend time in those places, not sitting in a campground somewhere along the way. Others differ in how/why they go to the north country. It is a great trip no matter how you do it.
On Edit: Did a quick check and S&Ts shows it to be just about 1,800 miles from Jasper to Fairbanks. Go east out of Jasper to just before Hinton, great KOA campground there, then go north on HWY 40, up through Grande Cache, they have a very good town campground there, then on to Grand Prairie and to Dawson Creek, several campgrounds there. From there just follow the Alaska Highway on to Fairbanks, actually have to use the last part of the Richardson Hwy between Delta and Fairbanks as they now claim that is where the Alaska Hwy ends. It used to be signed that Fairbanks was the end of it.
I have been driving to/from Alaska for the last 51 years and the roads are so much improved over what they used to be, that much of the challenge of the drive has been removed. You will see all types and all sizes of RVs on the trip. I have never found the type or size of the RV I was using to have any real effect on the pleasure I got from the trip.