I was once asked to catch Carp on a fly for a magazine article in the Field magazine and it was surprisingly good fun. Even a 5 or 6lb carp goes like and express train on a light trout rod and imitating bread flake with a bit of etha-foam on a hook is just about as simple as fly dressing gets.
Since that time I have caught Pike, Perch Dave and even small Tench on a fly and would highly recommend that if you have already learned at the trout, you take your fly rod when you next go out with your floats or ledgers.