I drove up back in aught-four. I grabbed me a Milepost and hit the road from Little Rock, Arkansas. The Milepost is an absolute must. The trip was incredible! I did it all with my wife, my 13 month old son, and a 140ish lb rottweiler. You can find a AAA book that's called "Traveling With Your Pet". It has hotels listed the entrie way up the Alcan that will let your cat stay with you. The Milepost is pretty reliable on this also. If you really want to do it right though, listen to AKfreighter and buy yourself an airplane and fly it up. You'll be kicking yourself in a few years if you don't!
Good luck!
Trouser