The transmission is often the weak link, not the engine. I note both Floyd and Norm tow(ed) their Scamps (13D and 16, respectively) with 4 cylinders and manual transmissions. They are not subject to the same overheating issues as automatics when climbing long grades at higher RPMs. I believe the Jeep has a CVT automatic.
Another factor that hasn't been mentioned is frontal area. A 1600 pound Scamp
is not the same as a 1600 pound tent trailer. Not sure, but I recall someone reporting that tow ratings under the new SAE standards assume 30 sq. ft. frontal area*. A Scamp
13 is more like 45 sq. ft.
A 4 cylinder automatic with a 2000 pound tow rating would probably pull a lightly optioned and loaded Scamp
13 satisfactorily in low elevation, relatively flat terrain at conservative speeds. If it doesn't already have one, an auxiliary transmission fluid cooler would be worth discussing with your mechanic along with the general durability and reliability of the transmission in this vehicle. I would want something more robust for mountain and high elevation towing. I would also want something more robust if I planned to check every option box on the build sheet.
As to attitudes and expectations, I take the position that towing a trailer requires accepting a slower pace of travel (regardless of cylinder count, transmission type, tow rating, vehicle brand or nation of origin, gender or eye color,...
). Even on flat, rural interstates in ideal conditions, towing speeds should be limited to 65 mph, and on long and/or steep grades trailers belong with the trucks in the right lane. Some states mandate slower speeds when towing.
*EDIT- Did some checking. Looks like the SAE J2807 towing standard for trailers in the 2000 pound class only assumes 20 sq. ft. frontal area. Here's an excerpt and a link to my source:
SAE J2807 Towing Standard