Towing with a Camry... Why not? I believe that in the USA, the Camry is rated upto 1000lb. Found an Australian list, and the Camry is rated for 500kg no trailer brakes, or 1200kg with trailer brakes. (500kg = approx. 1100lb, 1200kg = approx. 2650lb)
My suggestion is to make sure that you get trailer brakes added to your future trailer (even if you don't think you need them based on the weight rating). Your safety is priceless. Really, the only trailers that don't require brakes should be limited to those that do the 5 to 10 kilometre trip to the local dump with the yard waste.
For what it's worth, I have a Prius generation 3 and recently towed a Prolite Suite from Vancouver, BC down to San Francisco and back. Empty weight, the suite is 560lbs. Never got the time to weigh it with the camping stuff inside it. Put the Prius into power mode, and other then reducing fuel consumption, the car didn't even know it was towing. I normally get around 4.8L/100km (approx 50mpg) and towing I was getting approx 6L/100km (about 40mpg) (keeping to the country roads. On the I5, I was getting worse - about 6.5 to 7L/100km.
It was nice to annoy all the campers I met using their trucks to tow their one bedroom luxury apartments when filling up with gas.
Have fun with your camping trailer hunt, and enjoy your camping when you do get it.