Oddly enough, I don't believe any Barbie games were released for the Gamecube. Yes to GBA, PS2, Wii, and the PC, but none for the Cube -- which is fine because the Barbie game series is pretty poor anyhow.
I would suggest buying "Harvest Moon Magical Melody" (very easy to find, and you can be a girl in the game) or "Animal Crossing" instead. Lego Star Wars 2 The Original Trilogy is fairly satisfying for the younger set, and Princess Leia represents for girls pretty well. Anything with Mario will be a winner, and Chibi Robo is cute enough for girls to appreciate and not feel like they are in a world of boy games. Ribbit King too.
If u must buy a licensed property or movie based title, try Barnyard, Over the Hedge, Ratatouille (sp?), Cars. Barnyard and Cars both have very rich gaming experiences, and Ratatouille and Over the Hedge have co-op.