YES, definitely go to Dawson City. Everything mentiond above, plus the dredge, a really cool downtown, and the ferry ride is a necessary experience! Dawson is a throw back to the old days in the Yukon.
The Taylor and Top of the World highway from Chicken to Dawson City is a one of a kind drive with views unmatched on the Alaskan Highway.
This is NOT a trip to rush. You will want to stop and enjoy the scenery numerous times during your drive. Plus if the bear is not menacing the humans at Walker Fork, about 10 miles East of Chicken, that is a good place to spend the night, unhook and make the drive into Eagle! Then the next day after you enter Canada there is a pull out where you can unhook again and make the run to 40 mile. We ended up spending the night in the pull out in 2016 as a snow storm came through late in the afternoon. Do a little research on Eagle, Walker Fork Campground, and 40 mile. Those three places are worth the drive even if Dawson wasn't at the end!
Do check with the visitor center in Tok to verify if Walker Fork is open. They closed it early last week due to an adolescent bear bothering the humans!