First, I hope you're monitoring the weather closely and checking on the the post titled 'Roll Call Alaska 2016'. There's been snow the past few days on the roads further north.
This is kind of early for anyone to have done the TOW already so hopefully someone will chime in with their experience for this month.
However, we've done it with a 5th wheel and also a motorhome with no problems. Just watch the weather and if there's been a period of rain don't go that day. A couple days later it would be fine. One thing, if you get to Dawson and decide not to continue on you can always turn around...adding miles, yes, but if you don't feel right about it that's the thing to do. Dawson City is a fun little town with history. It would be a shame to pass it up. Or perhaps do it on your return later in the summer.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel