Weight distribution with a single axle trailer?

I see no reason for a WDH with a little trailer like that. It will be well within the truck's rating without it. As for sway control, if you load it properly that shouldn't be necessary either.
I've towed everything from boat to flatbed to RVs up to about 13,000 pounds. I've never had nor needed sway control. Except for once: I had a poorly loaded trailer behind a truck that was too small. Sway almost wrecked it.