Most likely your new camper is NOT designed for a weight-distributing hitch, and will say so right on the tongue frame work.
One sway bar is likely all you will need for belt-and-suspenders protection. Having a truck that outweighs the trailer and can easily handle the weight goes a long way toward preventing sway. I've also noticed that these lightweight single-axle trailers tend to have the axle closer to the rear, which also helps. Loading all the heavy stuff ahead of the axle is the final step you can take.