Are you talking about Lake Louise in Alberta's Canadian Rockies? If so, we certainly would not drive 300-400 miles a day to get to Fairbanks, Alaska. If it's your first trip to Alaska, there is lots to see along those miles that you'd want to stop for and explore. Also, the roads aren't interstate speed so you'll be going a lot slower...and you never know where you'll find road construction areas with gravel.
There are plenty of campgrounds along the way and many beautiful boondocking spots. How many times will you go to Alaska? For many, this is a once in a lifetime trip. Slow down and enjoy it!