.......as an example, below is a picture of both of my cars, the one on the left was built in 2013 and has a kerbweight of 1640kgs, the one on the right was built in 1957 and is a foot wider and nealy 2 feet longer, it's engine is a heavy cast-iron V8. Kerbweight guesses? 2 tonnes? Nope, try 3270 lbs (1483 kgs) due to a complete lack of gadgets and complex wiring that new cars now have.
You are fine, your car weighs the same as a mid to late 90's Peugeot 406 or Mondeo which used to be used for lugging MUCH larger caravans than you are looking at. The Fiat 500 (NOT X) shares the same floorpan as the Ford Ka and has a maximum towing limit of 800kgs and a lower kerbweight. Although the 500 & Ka share the same floorpan etc he Ka isn't type approved for towing. People tend to think that smaller cars are light, the reality is that todays smaller cars weigh the same as older large cars due to all of the extras fitted. As stated above, I used to tow with a 1998 Peugeot 406 1.9TD that had a kerbweight of 1340kgs, I towed all sorts, including trailers right up to its maximum towing weight and (apart from a lack of power!) it was fine.