We never gave our kids water before their first birthdays, and even then, we kept them on milk as their primary source of fluids until age 2.
I agree with SS that putting some in a sippy cup (water) to get her accustomed to learning to use it is a less messy way to teach her how to use one, but we were never advised to give water before the age of 1.
It's actually a point of contention I have with my sister whose daughter will be 2 in a few days - she gives her more water/day than milk because she's so scared of her daughter being obese. My sister is highly intellectual and professionally successful, but she's blinded by her own issues of being the "fat kid", and is making some questionable choices for her daughter.
The American Academy of Pediatrics actually recommends the initiation of solids between 4-6 months. Trust your pediatrician's guidance. Both of our kids were started at 4 months because they were consistently in the 90% on height/weight. It will depend on the child's ability to thrive and hit developmental milestones. Here's their position statement via their parenting website, HealthyChildren.org :
http://www.healthychildren.org/English/ages-stages/baby/f...