The basic FJ should have more than enough power to handle the smaller Airstreams.
Regardless of tranny and driveline configuration you get the same Toyota aluminum block 4.0-liter, 60-degree V6 engine from the Tacoma, Tundra, and 4Runner. With dual-overhead cams, 24 valves and VVT-i technology, the engine manages 239 horsepower at 5,200 rpm, and 278 pound-feet of torque at 3,700 rpm. Note that both numbers are based on 91-octane fuel, which isn't required but is recommended.
Preliminary mileage numbers are 18/22 for the automatic 4x2, 16/19 for the 4x4 with manual transmission and 17/21 for the 4x4 automatic. All models offer a 5,000-pound towing capacity, and an automatic 4x4 vehicle got to 60 mph in 7.8 seconds.
This charts also shows it is quite capable of handling 5,000lbs in an acceleration test compared to other vehicles.
One would believe the issue you would need to work on is stability. The links found in post #10 by REDNAX is your key to that door.