There have been a number of attempts to create a specialised search engine for kids. Yahoo did it - once Yahooligans now Yahoo Kids beta. Ask nearly changed to a kids site completely - or so the rumors go....
A new entry to the field is Quintura for Kids.
The space is a tough one and I think possibly one that has overreached itself. My 14-year-old uses Google... she would be insulted if she were told to use the kids' search engine.
Kids search engines should be for 3-10 year olds. After that they expect to be treated like young adults and the allure of cartoon drawings and puzzles just doesn't cut it anymore.