Draw an image of the duck on the side of a watermelon using a black marker. It doesn't matter if the marker is permanent or not. The lines will be removed once you start the carving process. If you are just starting out and not skilled with drawing, tape a coloring book page or a duck stencil on the watermelon and trace it.
Carve away the large chunks of watermelon that will not be a part of the sculpture using a carving knife. The sharper the knife the better. Any size knife will work, but one with a smooth blade is better than one with a serrated edge. Begin as far away from the lines of your image as possible and work your way toward them, shortening your cuts as you get close to your design.
Puncture the watermelon where your duck begins and cut along the lines you've drawn. Remove as much of the watermelon from around the duck as you can, leaving the green part (the skin) of the watermelon intact as you define the shape. When you've finished this process, you will have your duck image left, with surrounding melon removed. This gives your duck a three-dimensional look.
Detail your duck with a potato peeler. This will allow you to remove just the thinnest layer of dark green from the melon skin in selected places to give your duck some variation in color. Removing some of the top layer of skin on the duck's beak, wing and feet is one example of adding contrast. To do this, hold the potato peeler against the skin and apply light pressure as you skin down to the lighter color beneath the skin.