Enough muscle to pull our TT?

Pass the word... NEVER, NEVER, NEVER count the dry weight. This is what is used by salespeople to let you THINK you can tow a trailer. As soon as you drive that trailer off and start filling it up with stuff it will never be at the dry weight again.

Look at the trailer's GROSS weight rating. This is a better indicator because you hope you never fill it up with that much stuff because this is the maximum the trailer should weigh. But you must also subtract the weight of the extra stuff in order to tow the trailer, like the hitch, chains and a whole bunch of other equipment you're gonna need to tow that trailer.

Read the Gross weight, then compare it the the owner's manual of the tow vehicle (6500), then you must know how much everything else weighs.

Rest assured, a gas engine will lug as the maximum gross weights are approached. It's not about muscle. It's about many of the components of the vehicle (trans, differential, springs, shocks, drive shaft, shocks, wheels and tires, etc that can support the weight as you go up and down hills, bumpy roads and also be able to stop the load too. You may still need extra help like the trailer's brakes and a weight distribution hitch, but the dealer should have covered this with you.

Don't forget to include everything in the Jeep as you try and calculate this. Gear, passengers, pets, ANYTHING carried in the vehicle counts. This will also be the case if you upgrade your vehicle as you try and gain some "margin" for your rig combination.

Sounds like you've got a lot to learn. Learning this AFTER you've made your purchase means you are taking a chance.

as said the horse power is only a fraction of the equation. with a 6,500 pound towing capacity means you have 2,325 pounds left of that capacity. add a weight distribution hitch for safe handling and your campers dry weight is already increased without adding any people or gear.

then you add the weight of people, pets and all gear in the camper and Jeep. 2 adults, 2 kids and a large dog might weight say 650 pounds then clothing, food, cookware, bicycles, cooler with ice and other gear you can QUICKLY reach your towing capacity without realizing it.

filling the LP tanks and fresh water holding tank will further increase your gross weight coming even closer to or over the weight rating by the time you have all gear and people loaded.

generally speaking you should be ok but be conscious of everything loaded. that pack of paper plates, axe, fire poker adds weight.

Yes, do keep in mind the way the weight will be distributed. Like PhilnJim mentions you have 2,325 lbs, then subtract some to allow for the hitch hardware. This pretty much allows about 2,000 lbs of gear for the trailer like pots/pans/other kitchen stuff, bedding, food (or buy when you get there), water (or fill when you get there), tools for the trailer, one or two batteries, maybe even a generator and other tanks (drain before you leave and hope the dump station is CLOSE).

I hope the trailer has an equal or lesser GTWR (Gross Vehicle Weight Rating for trailers) than the Jeep. Besides the rear axle weight and rating, you'll also need to know the CGVWR or Combined Gross Vehicle Weight Rating. You can bet that 6,500 lb tow rating for your Jeep probably means the Jeep shouldn't be carrying anything. Here's an example, how to calculate this stuff.

The trailer (GTWR is unknown):
UTW - 4,175, unladen(dry) trailer weight (may not include some options and accessories added by the manufacturer or dealer).
CW - 1,500, cargo weight, EVERYTHING you put into the trailer, or installed in the trailer after it was built and rated.
GTW - 5,675, Gross trailer weight, hopefully below the GTWR and contents distributed properly.

The Tow Vehicle, (The Jeep, unknown GVWR, RAWR, FAWR, CGVWR):
UTW: 4,000 lbs, just what is in the Jeep and the fuel tank and all fluids topped off and you the driver.
GVW: 4,800 lbs, the wife, kids, pets, toys, munchies, travel items, other gear, and the trailer hitch hardware
RAW: Unknown, how much of this weight is over the rear axle? Will there be enough for the 10% to 12% of the trailer's tongue weight or 567 to 630 lbs ?
FAW: Unknown, how much of this weight is over the front axle?
CGVW: What about the combined weight of 4,800 lbs of Jeep plus the trailer weight of 5675 or a combined weight of 10,475. Does this exceed the rating which requires the frame, axles, wheels, brakes, suspension, drive shaft, trans, U-joints, engine, cooling systems, alternator and battery to support all this?

This is why knowing your weights and staying within these limits is important. Any part of being overweight means you are overweight. A vehicle operating near its maximum ratings will move slower, brake slower and struggle up and down hills and provide rougher rides than what your used to but if within weight ratings you should be good. Just don't push it!

Keep in mind, even big diesels break doing this. I belong to other forums and this is reported all the time. If even the big trucks "break" when they are within the proper ratings, why push it by being overweight.

I'd like to conclude that the purpose of this post is to educate, not create fear and disappointment. Realize that even if you get a bigger vehicle you must drive slower, brake sooner, shift later, make wider turns and tolerate the louder engine noises from the components trying to do their job. This has been going on for decades but the fun far outweighs a possible problem. If you minimize your problems, you'll maximize the fun! Simple as that.