Your child can snap as many shots as he or she likes, and is only limited by your camera's memory. Such ease gives a child the freedom for lots of experimenting about what does and doesn't work when composing a photograph. There's instant gratification. Your child can see what he's snapped without waiting for film to be processed. He or she can print out the results or email a file to family and friends.
Kids can be ready to snap a photo quite early, even at ages four, five, or six.
However, most aren't ready to actually take care of a camera until age six, at a minimum. And most aren't ready to download files onto a computer until age eight or older. My recommendation would be to wait until your youngster is capable of doing his or her own downloading, or you're apt to tire of the chore yourself. In any event, if your child is trying to take over your camera, it's time to get him his own. Luckily, you don't have to break the bank in the process.