How tall are semi-trucks, aka 18 wheelers? They have no problems crossing the border, as far as I know.
If you're still unsure, contact CBP Alcan or wherever you're planning on crossing, and ask them.
You can pretty much bet on construction along the route, and that means some stretches of gravel roads. They use pilot vehicles to control the flow, but they sometimes moved a little too quick for my liking, so drive at your own speed through the zones. Don't let them force you to drive too fast, if you don't want to.
The majority of the roads in Alaska were fine, for us. It was northern Canada that was a mess in spots. In August 2016.