A survey was taken a few years ago on this forum of RV owners who have actually weighed their setup. The average "stuff" people took was 1200 pounds over RV manufacturer dry weight. Larger families and full timers was higher and single and couples that take long weekends are lower. 1000-1500 pounds is a fair estimate.
The Jeep Grand Cherokee RV tow limit is likely the 720-750 pound receiver tongue weight limit. That puts you under 6k loaded. Also, at 585 dry TW, that is likely to exceed 720 pounds when loaded for a long weekend. As far as towing experience, a full sized half ton with whatever brand's HD towing package would be more comfortable.