Well, I would definitely start with the director. Set up a meeting so you have time to discuss the idea in depth and hopefully without interruption. Ask her what she would think of the parent group idea for the school and what she envisions as the group's goals and focus. Throw your thoughts out there and see if you can find some common ground. Then start looking for parents who would like to be involved in the group. With their help, you could begin to formalize the group.
Once you have some basic goals, set a meeting for all parents, teachers and the director and start building your group. You can find everything you could ever want to know about parent groups on this site and if you just post your specific questions, you're sure to get lots of tips and info.