welcome to the forum - its a great place to get answers and ideas!!
I agree with the payload comment.
You and your wife maybe 300 lbs, plus doggy and you're up to 350 lbs, and add in some gear and you're easily up to 400 lbs.
400 plus the 800 lb quad equals 1200 lbs.
Add a 100 lb WDH, and a minimal tongue weight of 750, and you're up to 2050 lbs of weight the truck needs to carry - and I don't think even the Max Tow with HD will give you that!!
That's 1 ton, and definitely Super Duty territory.
The WDH will redistribute some of the tongue weight aft to the trailer axles, but that will probably only be 150 lbs or so, in which case you'll still need something in the neighborhood of 1900 lbs of payload capacity.
If you could get rid of 850 lbs (WDH and tongue weight), then you'd only need 1200 lbs of payload capacity for the family and quad - and you wouldn't even need the HD package for that.
That's similar to the problem I had with my very low payload capacity in my standard tow, highly optioned King Ranch. I got a Trailer Toad that carries ALL
the tongue weight, so I have the complete payload capacity of the truck to load people and stuff in the cab and bed. With all the tongue weight on the Trailer Toad, the only limits I have are to not exceed the payload capacity of the truck by overloading with people and cargo, and not exceeding the GCWR (max combined weight of the truck and trailer).
Kodi - 2013 Kodiak Brown/Pale Adobe King Ranch SCrew EcoBoost, 5-1/2' shortbed, 4x4 and off road pkg, 3.55 locking diff, towing pkg, BakFlip Fibermax, PowerScope power telescoping Tow Mirrors, Amp Research retractable running boards