I would think that adding another sway bar on the other side would be adequate for what you want to tow. You may want to try towing the trailer with what you have now though before you add anything else. It may tow fine.
A single sway bar is usually good for up to about a 26 foot trailer. I would try it with one and see how it goes first. Your tow vehicle is not a large truck though so the addition of a 2nd bar would help a lot if you have problems.
Make sure your tongue weight percentage is good, tires aired up, and that your hitch is setup properly before you begin.
Barney
