Two issues I see. The rear "hitch mounting area" on the back of the Fiesta is only sheet metal, (not very thick at that) and as such, is nowhere near strong enough for long term stress of towing. It'll eventually tear out and leave you with big holes and a loose trailer.
The brakes on a Fiesta will be inadequate to reliably stop an additional 1,000-1,200 pounds of weight.
(As mentioned, the trans is probably not up to the task, either.)
I realize you wish to keep your fuel expenses down, but don't endanger yourself and other travelers to do it. Find yourself a decent V-6 powered Ford Ranger or Chevy S-10 with the extended cab. A Dakota would be better, but they quit building those in 2011, and by now, most of them would be getting a bit rough.
Now....about that GVWR. That 1,900# gets small rather fast. You need to subtract your weight, passenger's weight, gasoline weight (about 7lbs/gal.), cargo weight, hitch weight, and your pet's weight first. THEN the remainder is what you get to tow. (In case you're not familiar with how to calculate that figure.)
It MIGHT work ok, IF you could find youself a really light teardrop camper, but those get expensive if you're trying to buy one. There are folks building them on Harbor Freight trailer frames, with structural foam walls and bulkheads. I've heard of a few that got the basic build down to around 600-700 pounds.
Roger