What year, model and equipment is on the Jeep? Most Wranglers are incapable of towing anything that large. They are by far one of the worst vehicles on the road to tow with. Especially the 2-doors with their very short wheel base. They're meant to be towed, not do the towing.
A late model 4-door with the max towing package can tow the most, but even then it's only 3,500 lbs max. That's total weight, meaning the trailer can't weigh that much empty/dry. You add in any gear/supplies you load in the camper to it's dry weight which is generally several hundred lbs..
they make light weight ones they tend to be costly. But no matter even if its say under 2800-3500 for a 4 door. Still have a huge frontal area to deal with of the object in tow. Its a Box and even say a airsteam is still a rounded box. People tend to like the pop ups as they have far less frontal area.
2 door even with tow is only 2500. not much to say there. mainly for say 2012 up that means 3.73 gear option no matter for a 4 or 2 no option its less. 4d is what 2500 no tow and the 2d was 2k? i never think about jeeps towing much.
single axle 16' footish should have everything in it. be in around 3k if its one of those utrua light ones.
When we wanted a slide in cab over for our f250. even those can weigh tons. But they make very light 8' box cab over that is bone stock like 1900 dry. it might be at 2500 now with solar wet and loaded. I could put about 3800 in the bed but thats max would effect tow to much i need about 7k towing the jeep on a alloy trailer. plus that camper im just under the 10k total..... But that is a truck diesel.
My kid built a mini camping trailer to pull behind his wife’s JLU, and they seem pretty happy with it. It’s pretty small but big enough for both of them to sleep in it comfortably. It has a diesel heater, propane hot water heater, for hot & cold water at the sink in the cooking area. fans, lights, solar panels and a battery for off grid camping. They shower outdoors, cook outdoors, I’m not sure about the bathroom part. I guess you could take a little port-a-potty like they use in smaller boats.
As far as weight being towed behind a Jeep goes, I can relay my experience. I have a 2020 JLU Ecodeisel that is on the Mopar 2” lift and 35’s. I tow my 20’ bass boat with a 200 Mercury outboard motor frequently. I’m guessing when it’s fueled up and loaded for a day on the water, it probably weighs about 3K. It tows it OK, but you definitely know it’s back there. I wouldn’t suggest towing much more and still expect to be safe and feel comfortable.