IMO, power won't be a problem, but automatic transmission heat probably will be without that external cooler. I recently pulled a 14-ft covered flat that grossed 3350 lbs. with my '05 TJL 6-sp/4.0 using DC's OEM class II hitch setup and factory wiring. (Love the insulted electrical box in the end of the receiver - very nice design.)
Pulling around town, the engine has so much torque that I could barely tell the trailer was back there. Pulling up a 7+ deg. incline at 55 mph, I dropped to 5th to keep from overheating the exhaust manifold, and even with the cruise on, that AMC-6 didn't even break a sweat. I didn't have electric trailer brakes, but the unlimited is heavy enough and has decent enough braking that I didn't really need them. I normally don't insist on trailer brakes unless the trailer outweighs the pulling vehicle, and/or I'm pulling more than one trailer.
As someone else here mentioned, be sure you lock out OD, even on flat ground, watch your engine temp, and you should be fine. I should mention that I have a class ATX with 15 yrs. experience pounding the ground, which might have made it easier for me to work with.