The Denali Highway between Cantwell and Paxson is, IMNSHO, one of the most scenic roads in Alaska.
I drove from Paxson - Cantwell in 2010? 2011? while it can be muddy and or dusty, I went in early September (2nd week or so) and there weren't the bug problems. It was pretty rough in spots and I wouldn't recommend it for a trailer unless it was a pretty stout trailer designed for off-road. Not to say it can't be done, but lots of bumps, rocks, and gullies on that road.
As pointed out above, going in as far as Brushkana will give one a taste of the road and it is far enough back to get a sense of what the scenery and terrain is like. FWIW, I recall both the roughest road and the most scenic from 20 mile West of Paxson to about 40 miles East of Cantwell, i.e, the middle portion.