As others have said.... Short answer is ... No
Here's a little indoctrination on tow vehicles and travel trailers.
Tow vehicle's have multiple ratings involved with towing and their max towing capacity is limited to the weakest link. Normally, that weak link is payload.
GVWR ... Gross vehicle weight rating (max weight of the vehicle itself, along with driver, passengers, cargo in or on the vehicle, weight distributing hitch, and trailer tongue weight)
GCVWR ... Gross combined vehicle weight rating (max weight of vehicl and trailer combined)
Front and rear axle weight ratings ... Max weight on front or rear axle
Hitch receiver rating ... Max weight with and without weight distributing hitch. What the hitch receiver is rated carry. This is doesn't always correspond with the other weight ratings. It may be higher or lower than some of the others.
Payload (AKA max occupant / cargo weight) rating... The difference between the vehicle's actual weight, and it's GVWR. Capacity to carry everything and everybody in or on the vehicle. This info is normally on a sticker or decal, on the drivers door post.
It's not uncommon for SUV's to be in the area of 1200 lbs available payload. Frequently, they also have passenger rated tires, which have softer sidewalls, than an LT tire. Softer sidewalls lead to sidewall flexing and can cause trailer sway.
Max tow rating ... What the manufacturer says the vehicle could tow. This number does not allow for any aftermarket accessory, passenger or cargo weight. As those things are being added to the vehicle, its available payload and tow capacity are going down, pound for pound.
If you have a vehicle with 1500 lb available payload / 9000 lb tow capacity and you add 700 lbs of people and cargo, it's available payload and tow capacity become 800 / 8300 lbs.
Average camping load (dishes, pots and pans, groceries, camp chairs, bedding, BBQ, tools, spare parts, water, etc) is 800 - 1000 lbs. Larger trailers, may have more. Your 7000 lb trailer will easily pass 8000 lbs, when ready to go camping.
Travel trailer's tongue weights are on average 12 - 13 percent of the loaded trailer weight. Weight distributing hitches, weigh 80 - 100 lbs, and count against your payload, along with the tongue weight. Your 8000+ lb trailer will need up to 1200 lbs of available payload. Possibly more.
Whatever vehicle you select, will need capacity to carry combined weight of any aftermarket accessories (cargo carrier, bed cap, etc) added to the vehicle, any cargo in or on the vehicle, your family, and 12 - 1300 lbs of trailer / hitch weight. Towing at or above the vehicles ratings, can be very unpleasant. Leave yourself some cushion.
