I would rent a smallish TT before you buy one. You may be, barely, under your load limits, but would NOT be happy with the towing results.
I have towed with a Dakota pickup truck that had a 3.7L engine. I was well within it's stated limits, but that poor motor just screamed at me the entire trip. I would not do that ever again. The next week I had a 3/4 ton MegaCab diesel!!!
I'm not suggesting that you need to do that, but just be forewarned that the JKU will struggle. You need to experience what I did to understand.
Jerry
2015 Jayco Seneca 36FK
2011 Jeep Wrangler Sport 2 door
2011 R & R 20' Aluminum Enclosed Car Hauler
2007 Montrose 16' Aluminum Flatbed ATV Trailer