When you get to Whitehorse, drop in to the Visitor Centre and check the road conditions and weather forecast for Dawson City and/or the Alaska Hwy route. Make your decision which way to go and then plan to go the other way on your way home.
When you arrive in Tok AK, do the same. Check the weather to the southwest, around Valdez. If it is looking good, go that way first (when it rains in Valdez, it RAINS) so you can enjoy the good weather. Then carry on clockwise.
If the weather isn't looking so good at Valdez and the coast, head to Fairbanks and then carry on counter-clockwise & hope for better weather when you get to the coast.
The ferry over the Yukon River at Dawson City will run once the river ice is clear, regardless of the Top of the World Highway status. There are many people who live on the west side of the Yukon River and they rely on the ferry so it runs as long as it safe to do so on the river.
The stats for the start of the Yukon River ferry are here:
http://www.hpw.gov.yk.ca/trans/maintenance/george_black_ferry_stats.htmlMid-May is typical, with 2013's start of May 24 being one of the latest starts, other than 1967 when it didn't get going until June.