Not all body-on-frame vehicles are strong and not all unibody vehicles are weak. It's one of those generalities that can be over-applied.
For really heavy towing and hauling, yes, you want a body-on-frame, truck-based vehicle.
For a 1500 pound egg trailer, a well-designed, unibody, reinforced-for-towing, front or all-wheel drive passenger vehicle is more than adequate.
For towing the Burro, look for a vehicle with a minimum 2000 pound tow rating, more if you plan to carry extra passengers or gear. If you're not into SUV's, minivans can make good tow vehicles as they're built to carry a fairly high payload in passengers. A used one can be had fairly reasonably. Properly equipped, most can tow up to around 3500 pounds. You will need electric brakes
on the Burro.
Just be careful not to load too much in the vehicle when towing- with all that space, you can easily overload the rear suspension. But then, it's not hard to overload some trucks, either.