We have made the drive from Maryland to Alaska twice, 2005 and 2008. We have crossed at Portal, ND into North Portal Saskatchewan and at Sweet Grass, Montana. Either route was fine. We crossed at Sweet Grass in 2008 because of the high gas prices that year. In 2005 we drove the entire Alaska Hwy while in 2008 we drove to Prince Rupert and took the ferry up the inside passage. We have never had a problem crossing the border even with a dog. Just make sure you have all needed paperwork for yourselves and your pet.
The link to my travel blog from 2008 is attached. This blog does not include much in Fairbanks as we spent 5 days there in 2005 and saw most of the sights that year. Take several cameras. You and your traveling companions will want to take pictures and everyone sees each scene with different eyes. My husband and I will take the same picture yet they will be different. Also you don't want to miss a great shot because your camera fails. Have a back up.
We travel without reservations for the most part, except for Denali or if we are in a populated area on a holiday. Sometimes we would call a campground a day ahead as we were ready to move on.
Some parts of the road between Whitehorse and the border can be rough. Just take your time. Our only damage on two trips was a stone chip in the windshield of our tow vehicle.
I have used both the Milepost and Church's book. Both very helpful.
My husband is hoping for us to head to Alaska again next summer.