The Blueox Swaypro you linked is good, as is the
14k EQ or maybe the
12k EQ. For reference there is only
one Equal-i-zer hitch with different ratings. What you have is a basic weight distributing hitch that has optional friction sway control. My opinion is that 1000 pound bars is not enough for that TT and integrated sway control of EQ, BlueOx, and Reese strait Line are the minimum for towing a TT.
I've spoke with dealership and they claim I would be ok.
That statement comes up a few times every week on here, frequently followed by comments about how uncomfortable the towing experience is. No one has every said their truck salesmen has ever towed an RV. Yet there are thousands of RV owners right here that tow with all kinds of trucks. You don't have to listen to our experience, but where is the wisdom?
TV Specs:
6.2L EcoTec3 V8 engine 4WD
Curb Weight 5370 lbs
Max Payload 1805 lbs
Max GVWR 7200 lbs
Max Conventional Trailering, 3.73 Rear Axle 11800 lbs
GCWR, 3.73 Rear Axle N/A 16700 lbs 17700 lbs
Front Gross Axle Weight Rating 3650 lbs 3650 lbs 3950 lbs
Rear Gross Axle Weight Rating with 3.73 Rear Axle N/A 4100 lbs 4100 lbs
TT Specs:
MODEL 32-DBKS
Dry Hitch Weight 758 lbs. (344 kg)
Unloaded Vehicle Weight 8,703 lbs. (3,948 kg)
GVWR 10,902 lbs. (4,945 kg)
Cargo Carrying Capacity 2,215 lbs. (1,005 kg)
Exterior Length 36' 9" (11.2 m)
Exterior Height 11' 1" (3.4 m)
Exterior Width 96" (2.4 m)
Fresh Water Capacity 51 gal. (193 L)
Gray Water Capacity 74 gal. (280 L)
Black Water Capacity 42 gal. (159 L)
Awning Size 13 ft
That's 10k pounds loaded with a family's gear for a long weekend, another 500 with full water tank. That is also 1200+ pounds of loaded tongue weight.
There is no half ton I recommend for towing that TT. Should you proceed to tow that combo, your truck will exceed the GVWR, receiver, rear axle, and maybe GCWR. You are about to spend $40-$50k on a new truck. Spend $2k more on the 3/4 ton gasser, 4.10 axle.
From the words you use, it sound like you do not currently have this truck in your possession. Good. Get a more capable one with at least 2500 pounds of payload and 1500 pounds of receiver limit. Travel trailers are the most difficult type of tallier to tow. 10 miles or 150 miles. It's a huge box of air. They have two sheets of plywood to pull through the air at 65mph. They have 8'x32' walls that catch any wind that is not head or tail on.