Do I need an equilizer hitch?

No, you don't need one and if you tried to install one, it would be very difficult to set up.
Enjoy your new toy!

This time the dealer is...right.

With that particular combination I think a weight distributing hitch would be a bad idea. You want all the tongue weight you can get on the back of that truck to soften the ride.

Maybe for once on here someone will not say you need WD.
Why would you want to put more weight on the front axle that's heavier than the rear?

No WD hitch should be needed. But be sure to weigh your trailer tongue to make sure it's between 10% and 15% of the total TT weight; this is important for proper handling (avoiding dangerous sway).

I'd suggest to get one. Sure, your truck will handle the tongue weight, no problem and, if the trailer is loaded right, sway wouldn't be an issue. The tongue weight does unload the front axle of your truck, though.

I tow a 5K lb trailer with a 4x4 F250 with plow package. The plow package upgrades the front springs to 1 ton springs. I've towed without a WDH and the truck will handle it fine but it does remove weight from the front suspension. I like the steering axles to have the original load on them.

What does RAM say on the subject? If it was a GM product, they would state that no WD hitch is required for that setup and they might know a little bit about towing.

You are about to hear where it is so much fun to mess with a heavy, dirty, and noisy WD hitch that you will want one regardless of the loads involved.

By the way, the myth about front axle weight is still around from the old days when we towed with sedans and station wagons. A one ton diesel pickup has plenty of front axle weight bias. Note that manufacturers don't install ballast to the front end when they switch to a much lighter gasoline fueled engine.

If you decide to get one, I suggest you look at an Andersen for that size camper.

The wife and I made a trip out to Oregon and back to Delaware this past summer with a 23 foot TT and 2015 Silverado 2500 and had no problems with weight distribution or sway. You could consider just a sway control because any trailer can be affected by wind or big semi's passing. Again we didn't experience any issues on our cross country trip or traveling to New England and back. Our new TT is 29.5 ft, heavier, and more expensive so I had the camper dealer install a weight distribution/sway control system. And yes, they are freaking heavy!

Small trailer, big truck. You should have no problem without a WD hitch. Drop it on the ball and go.