Congrats on the truck and for reaching out to get some advice. I would just caution you to know the cargo capacity of your truck with the 6.7. Cummins before loading up and towing long distance. Sounds like you‘re moving house so you’ll be heavy I’m guessing. The heavier Cummins diesel engine is beast and can tow like a mother BUT can also eat up your cargo capacity in a 2500 truck. A 10,000 lb trailer Is heavy and I would guess your tongue weight will be over a 1,000 lbs which eats into the trucks cargo capacity - TT tongue weight, people, stuff etc combined weight. Towing is easy but you want to be able to stop and keep the vehicle under control while you’re underway. Second piece of advice make sure you have quality tires on your TT and have a TPMS on it.
You’re off to a great start, the auto level rear suspension is money well spent. You’ll have a pleasant tow experience and the ride will be cushy. Even though you have self leveling it’s definitely smart to use a WDH/anti sway hitch, my advice is don‘t ever tow without one. Since you’re new to this I’ll point out there’s a difference in weight distribution and sway control. Your truck has anti sway features built in but additional safety is important. Sway will vary dependent on size and type of trailer. If you’ve ever ridden a bicycle in the wind or carried a large flat object outside on a windy day you can relate to affects of wind and sway. The larger the TT the more surface area for wind to affect.
Weight distribution hitches will take the squat off the rear springs/air bags by distributing the weight partially from the frame of the trailer to the chassis of your truck. That causes the truck and trailer to ride fairly level and the front end of the truck/wheels to keep solid contact with the ground to ensure positive steering control. There are several good hitches on the market all claiming some advantage over others. The Equalizer has a huge reputation and seems to dominate the market. It’s made by the same company that also makes the Fastway E2 WDH. There is a price point difference between them but it’s a one time purchase, both are good products but the Equalizer is the king of anti sway control.
I pasted a video from a guy on YouTube, Big Truck Big RV, who does a good job in my opinion of explaining RV related tow stuff. He has a big following online and is a strong advocate for the Equalizer. Enjoy the video he has lots more on there that are informative. Feel free to PM me if you want, you’re headed my way. I’m located in Northern VA, let me know if you need any help when you get to the area.
Jim