First off, I think the FJ is a great vehicle, and I'm not at all biased because I have one...
Second, although there are some great threads with info on the topic in the Airstream forums, like this one linked here
(with Moses towing a 19' Bambi behind his FJ), there are also some really great threads on fjcruiserforums.com. In fact, I will be posting a new thread with details on how I converted my FJ to be more tow-friendly.
I have to echo TBRich's comments about the year. This is very important. To give you perspective, my 1959
18' trailer weighs about 2000# stripped and after renovation will be closer to 2800#. I believe the newer 19' models are closer to 4300#? And the rule of thumb is not to exceed 80% of manufacturer's rating, 5000# as per Toyota.
You will certainly want either a Weight distributing hitch or airbag inserts for the rear coil suspension. I went with the latter option because I also have been towing around some extremely heavy loads recently in the trunk, and have started using a hitch carrier with lots of weight on it. The Airlift bags took 4 hrs to install and completely level out the vehicle. This compensates for the FJ's springy offroad suspension when you need the strength.
The one thing I would consider if you are going to be climbing lots of hills and if you have a more recent trailer with more weight is the Tranny cooler. Everything else should be fine on the FJ, but that is the one place where you might want to extend the life. However, the fjcruiserforums have numerous threads saying that if you have a manual transmission then don't worry about it. I'm honestly not that familiar with manual trannys which is why I didn't even read a lot of those reasons or details. I do know for the automatics a few people have put coolers on (and I can never put it in "D" because that allows overdrive to engage).
Anyway, just my 3 cents.