You can tow with a short wheelbase vehicle. The trick is it needs to have a lot of weight. And that's pretty hard to do with most non-commerical or non-military vehicles. And they tend to ride miserably and aren't as forgiving of driver error or bad road surfaces (slickness, etc.) as a longer wheelbase vehicle.
"Could" an FJ55 be used? If it was me, and I was bound and determined to make it work, damn the topedos, I'd be putting in heavy duty axles from a full sized pickup, along with heavy duty running gear and a suitable engine. And then figuring out how to add as much weight (ballast) as possible with things like a heavy full roll cage, massive bumpers, beef up the frame, etc. By the time you've done, you're almost better off dropping a body on a home made or altered chassis.
The point is, I don't think you're going to do it well or for long with a stock FJ55. I wasn't even happy with my FJ40 pulling around my empty trailer made from the ass end of a full sized pickup. You could tell that the stock tranny really needed a lower 1st gear ratio with that weight. And my axle ratio is 4.10. Is yours 4.10 or 3.70?
Further, have you added up the weight of an FJ40 plus the trailer weight? Even with trailer brakes that's asking a lot of FJ55 brakes. Not only are you not going to have much "go", but not much "whoa" either.
And loaded tongue weight should be 10% to 15% of the loaded trailer weight. For argument's sake let's say the trailer and FJ40 weigh 6000 lbs (I can't find the empty weight of an FJ40 and my estimate is probably low). That means a tongue weight of 600 to 900 lbs. That's almost a half ton on your FJ55 hitch right there. You need a pretty herky suspension in the back to remain level, plus some ballast to keep some weight down on the front wheels for steering traction, since the hitch puts the load leverage way back to the rear of the natural pivot point, the rear axle. Your FJ55 frame and hitch better be up to the task back there at the hitch points as well as the spring perch and shackle points. And then there's the rear axle... I think you can see why I mentioned dropping the body on a custom frame. No doubt it would be the coolest tow rig, but do you want to go there?