A tranny cooler would definately help. It should be fairly easy to install. I know there was a TRD tranny cooler that was offered for the supercharged auto V6. Have fun driving cross country. I want to do that someday.
At the minimum, I'd get an external transmission cooler, they're not that expensive. Most damage to transmissions is caused by heat, so an external transmission cooler is good insurance. Check out http://www.summitracing.com, you should be able to find a good one for around $50. Installation shouldn't be too bad, you could do it yourself, or if you don't feel comfortable with the install, it shouldn't cost too much to have it done by a mechanic.
The 4cyl is rated to tow between 1000-2000 lbs (according to MSN.com), so you're right in the middle of those ratings.
I'd keep the speed to something reasonable, as your handling and braking abilities will be compromised by having the trailer in tow. In addition, if the transmission is doing a lot of hunting (shifting in & out of overdrive), you'll probably want to press the button to lock out O/D. On any decent size hill, I'd recommend 3rd gear.
Be sure to do an oil change and check all fluids before leaving, and continue to monitor your fluid levels (and condition) along the way. You'll be approaching the load limits of your tires, so you'll want to make sure they're inflated to their maximum pressure so they can handle the load.