You are going to come up against the "you need a one ton dually to tow a small 2h BP trailer" crowd. Get used to it...and ignore it.
That said, you do not want to tow a live load up to your vehicle's limit which I see you already acknowledge. If you choose a trailer with reasonable weight you should be able to keep things in the 5-6K range max and tow just fine. A WDH is a good idea and also recommended by Jeep for loads up in that range. While the JGC wheelbase is "only" about 115", that's still respectable for towing a smaller 2h BP trailer. And the vehicle weight is also up in pick-em-up truck range at about 5300 lbs.
I tow a 2004 Trailers USA Minuteman Sport 2h BP trailer with my 2012 Summit. (Hemi...diesel wasn't available then or I'd be driving one) The trailer weighs about 2200 lbs including the storage I installed. Our horses weight in the neighborhood of 1250 lbs each. So my load is under 5K with both horses. It pulls great. It stops great. (The latter is the most important part) Would I cruise the interstates constantly with this rig? No. But it's great for my needs which are largely local for trips to the horse park, local shows for my daughter and emergency use.
2012 Grand Cherokee Overland Summit - Winter Chill with New Saddle interior. 5.7L HEMI V8 - Nitto NT421Q "shoes"
Day-job...Telecom Technical Sales
Avocations...Woodworking, Equestrian, Food