Hey not to burst your bubble but i don't think UHaul will let you use their trailer to pull a car with a JK. It depends on how heavy the car is. It's not a matter of IF it can pull it (because it certainly can), it's a matter of controlling it while driving.
I know they would not rent me one to tow a car behind my XJ because it was too light in comparison to the car i was pulling
1995 XJ Sport
4.0L HO 5 Speed, 248,000mi and running strong!