Carol.,
We've used 3 similarly sized and
weight trailers all towed by the same tow vehicle.
None of the trailers came with an anti sway bar.
We towed them all initially without an anti sway bar including a trip from FL to NH with the
Scamp 16, a round trip to FL with a
Casita 16 and numerous trips with the Sunline 15.5, this easily adds up to 5000 miles.
We asked on the Sunline forum if we should add an anti sway bar and were told we wouldn't need it to control sway but might like it in an unspecified emergency. Since we knew nothing and it only cost about $50 we bought and installed one.
We've had two situations where we have had small emergencies, neither sway caused, where we were glad we had the anti sway bar. I have written about both on this site.
Hopevthis clarifies