The honest answer: it depends on where you start and how many miles you can stand each day with your crew. The Alaska Highway alone, Dawson Creek to Delta Junction, is 1,387 miles. Add your miles to Dawson Creek and the last leg to Anchorage or Fairbanks.
Simple math
From Seattle, it is roughly 2,400 miles to Anchorage approx. At 300 miles a day that is about 8 days. At 450 a day, about 6 days. From Florida, plan on well over 4,000 miles approx.
Speeds on the northern highway are lower than on an interstate, and you will stop for wildlife, road work and views. Most families do better with shorter days than they think.
Build in rest days
We like a rest day every three or four driving days. Whitehorse and Liard Hot Springs are popular places to stop for a day.