Just a heads up. Many Utah school districts have vacation from Thursday, Oct. 15 through Monday the 19th. We avoid going to Moab that weekend as it is very busy then. Many campers will converge on Wednesday to beat the crowds. If that is the weekend you had in mind, I'd arrive Wed. morning if at all possible. The BLM CG's along the river fill pretty quickly. The size of your rig limits the number of sites available to you.
There are other sites further away that might still be available Wed. evening. Horsethief CG off UT 313 on the way to Island In the Sky/Deadhorse Pt. SP tends to fill later. The BLM also constructed a new camping area called Ledges out Kane Creek Road with over 100 sites. The last four miles or so is graded gravel road that can get washboardy. This is probably the last area to fill. Turn off US 191 between the McDonalds and Burger King to get out that road.
Other weekends than the one I noted shouldn't be as crowded.