Ask your doctor. My daughter is a year old now, so she can have as much water as she wants, but I remember that when she was younger we were instructed to not give her more than a few ounces a day. Too much water can overload their kidneys and make them very, very sick. However, I don't remember what age water went from a "use with caution" thing to "apply liberally." I'd check with your doctor just to be safe. A runny diaper after giving her water is probably a sign that she had too much.