I haven't done it but it is commonly done from Bellingham, WA to Haines, AK you would still transit into Canada doing this route. The other option is to go to Whittier, AK to avoid travel into Canada. The Alaska Marine highway does not allow you to be on the vehicle decks during transit so you can't sleep in your vehicle, you will also have to rent a cabin or sleep on deck in the Solarium.
Expect it to cost well over 5K to do this.
I looked into it heavily in 2009 when moving a friend's family to Palmer Alaska. We said fuck it and drove a 26' Uhaul up the Alaska highway from Oregon in April. We did it in 3 days but that was two guys putting in miles trying to get somewhere. One day we drove 24 hours just stopping to fuel. Fuel stops are spread out a bit, so they require some planning. The frost heaves In the Yukon are a real bitch and will be hard on an RV if you try and do any sort of real speed through them. Also, the wildlife can be an issue.
You could cross in Coutts, AB and it's about 2000 miles to Tok, AK. You would join the actual "Alcan highway" in Dawson Creek, BC. Expect to pay$5-6 a gallon for gas in Canada.