The first "official" campground on the Dalton I think is Five Mile, by the Yukon river crossing, some fifty or sixty miles up the road and halfway to the Arctic Circle wayside/sign/camping area. If you pull the trailer that far, it seems to me one may as well go on and camp at the Arctic Circle. (Note: 5 mile does have drinking water and a dump station, the only dump station for many miles around.)
Frankly, in my opinion, many of the most beautiful parts of the road are farther north. Atigun Pass and the Galbraith Lake campground not too far beyond had some of the most spectacular scenery I saw anywhere on my trip to Alaska. (Galbraith lake campground, it should be said, is a couple very, VERY bumpy miles off the highway. It's a passable road, but plan on a half hour or more at a crawling pace over the washboards.) Other areas also had incredible views. Much farther north and it changes to more rolling, flatter tundra, which is quite beautiful in it's own way but not as awe-inspiringly spectacular.
If you're starting out from the Fairbanks area, maybe you could leave the trailer at whatever campground you're staying at there and take a (longish) day trip to the Arctic Circle sign, if that's really the main destination of interest. I would suggest getting a meal at the little cafe next to the Five Mile campground because everyone you talk to afterwards is going to ask if you ate there!