I've been on safaris a couple of times, and if I had children I wouldn't take them until they are teenagers. While seeing the animals in more contained areas like the parks in South Africa might be okay, the more rugged safaris would present too many problems for me with a child. Also, they are pretty expensive and unless you were positive the child would enjoy all the aspects of it, I wouldn't spend the money!
I loved my adventures in Kenya and Tanzania and they are great great memories!