I would not recommend carpeting the new piece, just fiberglass a piece of marine grade ply. Carpet will hold water and mold and will just advance the roting process. Also, if you fish the boat, carpet will hold the fishy smell. Unless the whole cockpit is carpeted and you are trying to restore it that way, I would not recommend carpet. A fiberglass deck is the way to go if you are going to put the work in.