We drove it a couple of weeks ago. The entire two days (we stopped overnight) threatened rain and/or drizzled. We were in our 34' class A towing a jeep. We had absolutely no problems - in a car and truck camper, you will have less.
There is only about 13 miles that are 'bad;' the miles right after Chicken. The rest of it is simple. There are a couple of tight spaces, a couple of really bumpy roads, quite a bit of dusty gravel.
Our first day, we drove from North Pole to 10 miles outside of Chicken. The second day we drove from there to Dawson City and arrived around 2PM after stopping quite a bit. We passed 2 class As larger than us just past Chicken who were going the other way. They had no problems either.