Designing for kids or a younger audience often requires some changes in the style of design that is required. Because children are often more visually oriented and readily make associations between images and concepts as opposed to words and concepts, image or icon based navigation tends to prevail.
Additionally, the use of graphics that create a virtual environment tend to engage younger audiences and encourage them to explore the site. Many of the most popular kids sites are learning oriented, and use these principles well. Check out these examples of web design for kids.
Warner Bros Kids
Pop Cap Games