For your plug I recommend this one: Hopkins Tow Package Wiring Kit for Toyota Tundra Hopkins Custom Fit Vehicle Wiring HM11143395
It is made by Hopkins, I run one on my truck, I love it because the terminals in the plug are potted, which means they are sealed in epoxy, this means they don't corrode, and most of the normal trailer wiring problems are non existent. Not only that but this version for your rig is plug and play.
Before you do any long distance towing I would strongly recommend that you do some practice towing with out your horse in the trailer. Get used to the trailer and how it tows, then put your horse in and practice more.
Your Tacoma should do the job, but keep in mind it is still a pretty light duty truck, I have no idea what your trailer will weigh loaded up but keep in mind it is possible to overload that truck with out trying too hard.
Oh and a little goodie I always recomend to people is this guy: Fastway Zip Coiled Trailer Breakaway Cable - 6' Long Fastway Accessories and Parts FA80-01-2160
It is a self coiling cable for your break away, they are way better than the one your trailer came with.