We are going through the exact same thing right now. Morning and bedtime feedings only (today was our last morning feeding, though). I keep milk in a sippy cup in the fridge and offer it every hour. When DS is thirsty, he drinks a bunch of it and when he's not, he turns his head. I should add that when he has refused/drank just a bit for 2-3 hours, I'll tip the cup up for him to get the flow going. He'll drink more that way. Eventually, he'll be totally in control of the cup, but as of now I want to make sure he's drinking enough.
She'll get used to it, and will probably adapt quickly once you quit. If you are worried you can include juicy fruits in her diet for more water - watermelon, grapes, etc.