A golf cart weigh less than 1000lbs. Your Jeep either has a 4.0 litre six with a 42RE trans or a 4.7 V-8 with a 545RFE trans both can handle the trailer with no problem. Since it is flat land from SE Lousiana to FTW you will be fine. If you feel the Jeep laboring up hills/the bridge over mobile bay or shifting constantly take it out of overdrive (push the button on the side of the shifter) if not leave it in OD.
PS... having the cruise control on will also change the shift pattern(upshifts at a higher RPM and downshifts easier)
28 years as a tech at a Jeep dealer comes in handy
Jeff
I highlighted this because this is exactly what my dh said, if my dh says you'll be fine I beleive it ! You're going to be ok, just drive safely and have fun ! If your really uncomfortable about towing ask on rv.net they will really have at it and let ya know .