I don't know what my teardrop weighs off the top of my head. Probably more than 2,205 lbs, but probably less than 3,500 lbs. I certainly haven't noticed any issues with towing off road, but I don't go rock crawling either.
While the 7,716 lb tow rating is certainly higher than a typical midsize SUV, I probably wouldn't use an LR4 regularly for anything over 5,000 lbs through the mountain west where I live, work, and play. There are definitely times when I feel like I'm flogging it to maintain a safe speed up steep high elevation grades. Given the LR4's tendency to need a close eye on the cooling system anyway, I just wouldn't want to use it for really heavy towing all the time.
Also, another reality is that a V8 LR4 is going to consume a lot of fuel, and that consumption will become downright obscene with a heavy trailer. Plus, it only has a 22.8 gallon tank with the computer reading 0 miles to empty after consuming about 20 gallons. Range anxiety will definitely become a part of your trip planning.
I love my LR4. It feels very safe and sure footed towing, but I'm not blind to its limitations either. I have no idea what your camper weighs, but if it has large frontal area or weighs around 5k loaded for a trip, you may wish to look for something that has a bigger fuel tank and is more geared for towing.