Check the following message from a Camry owner towing 900 lbs
responding to towing tent trailer. BTW, the manual should tell you.
IMO the Camry is good up until 50% of the passenger weight rating.

Re: 2001 Camry Trailer Towing [gerryd] by joescar
Jun 26, 2005 (8:56 am)

Replying to: gerryd (Jun 25, 2005 5:35 am)
We towed a 900 pound pop-up with a 4 Cyl. Camry and although it didn't
do any damage, I'd have to advise against it. Stopping was difficult,
the suspension was strained, power was inadequate, etc. I would
certainly NOT tow the weight you propose under any circumstances! Buy
yourself a truck or SUV if you want to tow. A modern van is also an
alternative which worked well for us. Best of luck!

If it is now and cold on flat it should not hurt it but in high temps
up mountains it will he hard on it, heat kills transmissions. Total
weight should not be much but what does the trailer weigh and full car
load. You have to KNOW how to balance a trailer, or stopping can be
impossible.

I towed a 1000lb 14' boat, trailer & motor with 90lb tongue weight for 300
miles x2 times per year on Wisconsin highways (mild hills) without any
problems with my 2001 Camry 4cyl. Auto. I used a class II hitch and had 3
people and some luggage in the car. Temps in the 80s to low 90s. Car never
had any issues. Towing capcity was rated at 2000 lbs. I was getting 21-22mpg
when towing. I changed the tranny fluid every 15k and changed the oil every
3K. I'm sure towing puts extra wear on the  engine and tranny, but I never
had any issues in the 4 years I owned the car. I have a 2005 4cyl Camry now,
and pull a small trailer with 2 scooters occasionally, and have no problems
with this setup either. Towing the scooters is almost unnoticeable compared
to the boat, but the car handled both well. I had a F150 and pulled a stock
car years ago, and I would say the Camry towing setup seems just as capable
within it's limits. The trailer also comes in handy for lumber or other
large items I need to haul once in a while. Some of my macho friends insist
they need a pickup truck (14mpg) to haul the same load 2x per year and their
mouth drops open when I explain that I just use a trailer (30+mpg hehe).

Drive safe and leave plenty of extra stopping distance, and don't forget you
are towing when changing lanes.

Reb