Unless you are planning to drive directly from Fairbanks to Dawson City the main Highways in Alaska and Yukon are all paved and pretty well maintained. However, not all the Winter damage, (e.g. frost heaves), will be fully repaired yet but those areas will be well marked before you hit them. The Alaskan portion of the route from Fairbanks to Dawson City via the Taylor Highway #5 is unpaved and open only in the summer. Once you cross the border into Yukon it is paved and in generally good condition. sometimes rental car agencies won't let you drive on gravel roads so if you are planning to drive the Taylor Highway best let them know.

Personally I think going that using that route (i.e taking the Taylor Highway to Dawson City), is worth the bumpy six hour drive to the Canadian border both for the great scenery and also by taking that route you're able to to a circle without doubling back as you'ld have to do if you took the Alaska Highway to Whitehorse and then Yukon Hwy #2 to Dawson and then back the same way.

While the calander will say summer and the days are over 20 hours long it can still be quite cool at that time of year especially on the higher elevation parts of the route. So yes - take sweaters and warm rain gear.

In Dawson City don't miss Diamond Tooth Gertie's saloon and Gambling Hall which I believe is the oldest continuously run Casino in North America. For most of the trip the scenery is probably the main attraction.