Not only would I carry a spare, you might want to consider carrying two. I carry two, although I have a tandem trailer, since the possibility of loosing 2 at once are greater with a tandem. Don't forget the obvious; a lug wrench, jack, plug kit and 12v compressor. A spare set of wheel bearings are cheap, so if you can, bring a set. The chances of those going out on a long trip are incredible.
Don't forget to pin the radiator fan of the rear facing Pilot to stop it from spinning backwards. I usually take a Zip-Tie and push it through the fan guard plastic to keep it from spinning. Use the biggest one you can and don't worry about getting it "locked". I've never had one fall out and if it isn't locked onto something, it will allow it to spin free if you forget to remove it before riding.
Once last thing I want to mention that I have used is the safety chain links that are of the removable locking variety. I don't know what the name is but it's a replacement for the "S" hooks on the trailer safety chains. It has a bolt type closing lock that is tightened with a wrench. It can't bounce out like the "S" hook and it makes it a little harder for thieves to walk off with you trailer.
