Oh my, my favorite system and topic! I just love it when people come in at work and want suggestions for Gamecube. First and foremost, look at nintendo.com as they have all thier games there and you can get a better idea it our suggestions are on par for your DD.
I LOVE Annimal Crosings! It is truly a super neat game that even you might want to play with her. You do errands and such to get money and furniture. Eventually you catch fish and bugs and either sell them or donate them to the museum.
Donkey Konga is new game that everyone is raving about. It comes with a set of kongas and is very interactive.
Mario Kart Double Dash is a cute racing game that is suitable for all ages.
Paper Mario 2 is one that I have not seen, but know is supposed to be real popular.
All the Harry Potter games are good, if she likes HP.
I also like Mario Golf and Zelda.
Also, she can always use memory cards, extra controllers, and if she has a Gameboy, something called a Gameboy Player. It allows her to play all of her Gameboy games on the Gamecube. I strongly recommend only using Nintendo made products. The generics are cheaper, but we do get a lot of returns on them at my store.
As far as the ratings go, you can look at this
http://www.esrb.com/ to get a better idea on the difference between "E" and "T" I feel that there are some of the "T" games that are OK for 9-10 year olds, but that is my opinion. If you have any questions, feel free to ask, as this is what I do at work every night.