It'll definitely move it with confidence, in my opinion. I have the same tractor and am looking to move around all my trailers which includes a 21' 4400 lb jayco. Camper tongue weight is usually under 1000 lbs, your kioti will lift and move it with ease.
However! as others have noted, you wont be able to see around it easily when driving straight. I am curious if pausing motion, standing up and leaning way out to the side while staying on the tractor will be good enough to get a view down the sides. I need to park my jayco under a metal carport, tucked right to the side.