That is a lot of driving for a 'short day trip'. :B B.C. is huge, I have still not seen anywhere near all of it. There is a lot of information here regarding travel on the Alaska highway. If you want to set a toe in the Territories turn north to Ft Liard then go back to the main highway to continue north west into the Yukon to Whitehorse.
Now you need to make some decisions. You can carry on to Alaska if time permits or go north to Dawson City. If time is short return to Watson Lake then turn south back into B.C. At Meziadin junction go into Hyder so you can say you haave been to Alaska. Watch out for the local adult libation, that stuff will curl your toes.:B