Alicia:
WOW! 9 days to play in the parks! With so much time, you can enjoy a leisure pace and plan around the crowds!
I'm a little handicapped not knowing your specific dates, but using some of my tips for choosing which parks to visit on which days (found
here), on your first day, check in, familiarize yourself with your resort, and then head to Disney Studios to catch Fantasmic. I suggest Disney Studios because it would be better to visit it for its attractions on one of those other three days when Fantasmic isn't shown, helping cut down on the crowds. If it's not shown the night of your arrival, I would strongly consider going to Magic Kingdom your first evening and shaving off one of your full days (nothing like beginning your vacation with a stroll down a full-lit Main Street U.S.A.!) or going to Epcot to enjoy a meal at one of their many restaurants and catching Illuminations! All these choices will kick off your vacation with a BANG!
Animal Kingdom should only take you one of your full days, and I suggest it on a day in the middle of your vacation when you need a shorter day of activities and some rest.
Epcot usually takes two days to enjoy, but with the age of your daughter, you may be able to cover it in one full day and then a portion of your last one (if you didn't choose it for your first night).
With the age of your daughter, don't make that 9-day ticket make you feel like you've got to spend every day at a park. I bet all of y'all would enjoy relaxing at the resort pool (I suggest Sunday when the parks are crowded) or taking an evening stroll at Downtown Disney and sharing a banana split at Ghirardelli's Soda Fountain!
Wishing y'all a magical vacation!
Whitney