IIRC the SV304 is almost 37 feet and has a gross weight of 10K. It probably will be close 9K fully loaded, but without water. You really should get an actual weight on yours loaded up to go camping as that is the only way to know. Most people are surprised, but not pleasantly, when they get actual weights on their rig.
For this example, again since you don't have actual weights, lets figure 9k and tongue weight of 1125 (optimum 12.5%)
according to trailer life the tow rating on the 8.1 is between 10,900 and 12,000 depending on rear end, 4wd and other options. so that should check out well for that rig.
However, knowing several people over the years with the 2500 Burb, the payload rating is not close to the pickups. I would be a little concerned about that.
You need to look at the door sticker for the truck you are looking at for payload figures. with a curb weight around 6K and a GVWR of 8600, there is not as much payload available as you might think.
2013 Coachmen Freedom Express 320BHDS pulled by a 2005 F250 King Ranch CC
A rainy day camping is better than a sunny day at work.