Your vehicle has several ratings you should understand with respect to RV towing. No one tows and empty RV more than once - when purchased new and empty. At 7800 pounds dry, it will likely exceed your tow rating at 9000 pounds when loaded with a long weekend of gear and a full water tank. 940 pounds of dry tongue weight will likely be in the 1100-1200 pound range when loaded. That will likely exceed your receiver rating as well as payload of the big Q. I would not tow that TT with my Suburban which has every towing related rating higher than your Q.
So how much weight should you consider? It is wise to stay below all your vehicle's limits - GVWR, axle, receiver, and tow rating. Take a look for a sticker on the receiver itself for a limit. If not there, then the owners manual may also list a tongue weight limit. I thought yours was in the 900-950 pound range when using a WDH. Here is a sticker from mine for example:
Most to all of the tongue weight is supported by the tow vehicle's axles so it is considered against the payload of your vehicle. Every 2006+ model year vehicle sold in US/Canada has this sticker usually posted on the driver's door or door jam for how much payload is available with the exact equipment from the factory. Note what your has wat mine says 2051:
Take your number, subtract your estimate of people and cargo inside the SUV. Take the lower of that or receiver for what is available for TW. Multiply by 6.5 for a reasonable dry weigh estimate. I suspect you'll end up close to 6000 pounds which will make for a comfortable towing experience. Get a WDH with integrated sway control and proportional brake controller. Make sure your Q has the proper heavy duty towing equipment which I believe includes the optional shorter gears and large capacity transmission cooler.
