You should not have any problems with such a small trailer. The factory tow package comes with the larger diameter sway bar (21mm vs. 17mm) and provides some additional lateral stability.
If you have any issues with a light trailer, it will be the fact that such a light tongue weight might cause a "teeter-totter" effect on the hitch ball, causing the rear end to jerk up and down on uneven roads. Obviously, load the heavy cargo towards the front of the trailer.
Lateral movement can usually be managed by increasing tire sidewall stiffness, by using a higher tire pressure (read your sidewall regarding PSI) and/or using a light truck (LT) or C-load rated tire. In addition, your suspension bushings have got 7+ years of wear on them, and may be worn or soft, that may create some rear end wiggle.
Check the condition of your brakes.
Click the shift knob to "4" if you are traveling over repeated inclines. It will be easier on the transmission if it isn't switching back and forth between 4th and 5th gear, and the engine will be maintained in a slightly better powerband.