As eventerbabe pointed out, you are getting close to the tow capacity of your vehicle. Don't forget to factor in tack, hay, water, etc to the wieght. While you may be OK, there are other factors to consider.
Ideally, you should speak with a knowledgeable car or trailer dealer. Towing too much, or towing improperly can leave and your horse stranded on the roadside, or worse yet, get someone hurt.
Aside from tow capacity, you should also check you "maximum gross vehicle weight." This is the max weight of the car, trailer, passengers, luggage, etc. that the car can handle. It is possible to be within your "max tow capactity" but exceed the total weight the car was designed to handle.
Also check your transmission package. While your car may list a tow weight, that may be with an optional transmission, or other optional accessory. Most problems I have heard of involving towing have been failed transmissions - this can happen even keeping within the suggested weight limits.
How much and where you are towing is also a factor. Once a week to a local destination? You may be fine if you are near (not over) the weight limit. Up and down hills? Frequent towing to shows? Going long distances? Then you should really look into a truck designed to pull a horse trailer.
I recently went through this with the car I just bought. We didn't want a big truck or SUV, but still wanted to pull a two-horse bumper pull. Based on the points noted above, we decided to go a different route. We bought a car that we liked. For the infrequent trailering we plan to do (when we actually get a trailer) we will simply rent a truck to pull it for the day/weekend. There are also other people at my barn that often have extra trailer space that I can use. My new car is on a two-year lease. The trailer hitch would cost another $1,200 installed - it is also less expensive for me to rent for the few times I would need to tow over the next two years.
Hope this help or gives you some ideas.