Your vehicle is specifically designed to tow up to 2250 lbs so towing less should not be a problem. You may have to replace your transmission fluid more often because towing allows the transmission to get hotter, and transmission fluid wears faster based upon higher temperatures.
Your vehicle is already equipped with a transmission oil cooler. You can follow the cooler lines going out of the top of your transmission and into your radiator. Your radiator has a tube that allows the transmission fuild to flow through it so that it can be cooled. I have provided pictures below:
Please let me know if there is anything else I can do to assist you.
You will be looking to pay $100-$150 to install the transmission oil cooler.
I don't believe that it will be necessary for the minimal amout of towing that you are doing, unless you tow the trailer every day.
You will probably replace the transmission fluid every 30,000-45,000 miles depending on the fluid condition. Transmission fluid wear is based upon heat. The general rule of thumb is that a 10 degree increase in trans fluid temp. causes the fluid to wear 10% quicker.