It will be fine. The bodyshell is the same whether the car was sold in Europe (with their tow rating) or ours. The ZF 8HP is more than strong enough (if you bought a Ram truck, it would have the same transmission in it - built by someone else, but same design).
Trailer brakes? The Euro tow rating will assume the use of trailer brakes. That's one thing to be careful about. My european cars (VW) were limited to 600 kg without trailer brakes, much more with trailer brakes, and I wouldn't want to tow much more than that without trailer brakes. It isn't that the stock brakes aren't up to the task, it's simply that with a heavy trailer you have more of the total combined weight on axles that haven't got brakes ... the remaining axles that do have brakes, become traction-limited sooner.