Trip from Calgary, AB to Alaska

You can go west to Banff from Calgary and then up the Ice field Highway to Jasper then east to near Hinton and north through Grand Cache onto Grande Prairie and then onto Dawson Creek and the start of the Alaska Highway as others have suggested or head straight west over the Rogers Pass through Revelstoke, Kamloops and north to Valmont through Mt Robson and onto Jasper and then that way. If you go up the Alaska Highway make sure that you come back on the Stewart Cassiar Highway a very beautiful trip also.
The new Milepost is definitely a great travel guide, the trip to Alaska is an unbelievable trip, please enjoy. The roads are not super highways but with patience will be no challenge.