Since it has pretty much stock size tires and no lift take it to the dealer for warranty.
It is probably the onset of death wobble. Usually Jeeps that are lifted over 3-4" will get that, but it has happened that bone stock Jeeps will get it too. It is usually caused by track bars, bad shocks, bad tires/balance or bad bushings in the front end. I personally feel that sometimes it is caused due to slight variances in the assembly of the brackets on the frame and axle.
A larger steering stabilizer might help some, but I would really try to solve the problem instead of lessen the symptoms, if possible. A larger steering stabilizer is a good idea if you are running bigger than stock tires, but it probably isn't needed in this case (though it wouldn't hurt).
P.S. If one dealer won't do anything, go to another. New car dealers are horrible about doing warranty work. They are usually too lazy to look for service bulletins and don't care enough to try to fix it since they would rather keep the racks full of out of warranty rigs paying full price for repairs.
