Sounds like you are towing a Bambi travel trailer. The 16' has a GVWR of 3500 lbs plus your gear. To keep a 4000 lb travel trailer civil, it needs a load sharing hitch with an anti-sway feature. The short wheel base should not be too much of an issue - but don't plan on running the speed limit. You can plan on 10 - 12 mpg.
The most important part - have fun in your FJ!