The other issue is braking. I had a little 4-cyl. Geo Tracker, and it was fine towing my utility trailer with our lawn tractor and some yard equipment, when we'd go take care of the MIL's yard.
But, I loaded it up with some free manure that a stable was getting rid of, and they dropped a bucket load in the trailer (not sure of the weight), and it towed fine, until I went to stop.....then, I realized just what all that extra weight meant to the brakes. I did stop, and didn't have any panic stops....and drive with lots of room between me and the cars in front.....made it home safe and sound.
I'd recommend a braking system with any larger towable you get....such as a P'Up. You'll be glad you did.
I agree that you will be putting a strain on the tranny and engine, but it's your car.....and you may find that once you start camping, you want to upgrade, and you'll be upgrading the tow vehicle too.