We went up there a couple of summers ago with a Nissan Armada pulling a Passport 2400BH, which is a heavier trailer than yours. We didn't do much special other than gas up and go. There will be slow spots, especially the last climb from the Brainard Lake intersection with highway 72 at Ward. Take either Hiway 6/119 out of Golden (Clear Creek Canyon) or Hiway 119 out of Boulder to Nederland. From Nederland its highway 72. All good road, though climbing either canyon is a continuous climb with lots of curves as the road follows the water. You will also have some company. I would not recommend Left Hand Canyon Road out of Boulder as you can run into lots of cyclists and the section through Ward is steep and narrow.
The road into Brainard Lake is a secondary paved road with a 30 MPH speed limit, and you will find you can't go much faster as its a good climb. Not a bad road though.
Pawnee is a very nice campground, but you need reservations. There are only a couple of first come-first served sites and they go really early, if any are available. You want to be in the west (Elk) loop, that has trees. The east (Moose) loop lost all of its trees a couple years ago due to a winter micro burst that blew down the trees. So the Moose loop sites are have little or no shade.
Don't know if you are a hiker, but if so try Blue Lake if you are up for it. Its 3 miles in with a 900 ft climb, all above 11,000 feet. The trail gets pretty rocky (it is the Rocky Mountains after all). A shorter and less strenuous hike is to stop at Michell lakes, only a mile or so in and the trail is not as rocky as it gets once you reach tree line. The trail head is a couple mile drive from the campground, and the lot fills early. Plan on being there by 8 or just after lunch and hope to find some spots as people come down.