Watch this! Here's a 5 year old that can really play the Ukulele quite well.
From Topless Robot:
Meet Uke3453, the 5-year-old ukelele-playing sensation, performing his cover of The Beatles' "While My Guitar Gently Weeps." It may be the most phenomenal thing I've ever seen, mostly because of the way he rocks the fuck out near the end. It's so simultaneously adorable and awesome I can barely stand it. There are several more videos at the link.
Japan has a lot of great child musicians. Here's an awesome 6-year-old on the piano: