Jonell,
Congrats and welcome to the camping addiction... I mean world. Many of us here have had a lot of camper and towing experience and towing with a vehicle not up to the task is always a concern. On pure numbers, you should be OK. But like Ed said, there are a couple of other things to consider.
Can you tell us a little more about the camper you bought and what you are towing with? What vehicle, engine, tow package or not. Just because your car/SUV/whatever may not have come with a "tow package" from the factory, it can probably have things added to make it more competent. Some factory tow packages only give you a hitch and maybe a trans cooler. Others have bigger radiators, batteries and other things. Hitches and trans coolers are easy additions. Bigger radiators are a little harder, but if you have/add an external trans cooler, that gets a lot of heat out of the radiator too. (most automatics have a trans cooler built into the radiator)
The best thing you can do to help with piece of mind is to take your camper to the scales. Most truck stops have scales. It sounds crazy, but go across with the trailer hitched and again without the trailer, then do the math. A lot of folks say to only tow up to 75-80% of the tow rating. It does make you feel more comfortable towing way under, but I have towed right up to the limits in several vehicles and it doesn't feel much different. That's me though and I tow a lot of things all over the country, some really big (21,000 lb, 2 car race car hauler) and some really small (T@b trailer for friends).
Last thing, read through the owners manual for you car. I had a V8 Explorer that had a 8000 lb tow rating, but it also said in the manual that the trailer needed to have less than 49 sq/ft frontal surface area. It wasn't the over weight, but also the drag (wind) that mattered. I towed a 33 ft, 7200 lb TT with that Explorer. It needed dual sway controls and a big trans cooler, but it did it for 168,000 miles until it was hit by a semi and totaled.
Hopefully, you aren't scared off by now. Like I said, being 23% under your tow rating should be plenty of comfort. Knowing all the numbers helps put it into perspective.
j