Grand Cherokee will tow better than F150 (lower center of gravity, short rear overhang, independent suspension). I agree with Hazman65 - the hitch setup is the key. Looking at how people are towing, most people do not understand this. Then you read over the forums that half ton cannot tow anything and 3/4 ton is needed to tow any trailer.
Your trailer is fairly small and light. You should be careful not to go over axle and tires limits. Personally, I do not think payload is that important - just my opinion.
For completeness, I am towing 33' trailer with BMW X5. 20k towing miles. Tows like on rails. I am using ProPride hitch. Super stable.
https://youtu.be/slIqVsGuIn8