Skip My Secret Diary -- pretty poor quality -- can't do much with it.
Princess Debut by Natsume if u can score it for $19.99.
Animal Crossing. Nuff said.
If she likes Pokemon, any Pokemon game will do, but she might not be into it -- ask first, as she might think it's a "boy" thing, though lots of girls do love Misty and Dawn, and my little girl and her girl friends love anything Pokemon.
If u go the Imagine game route, choose carefully: Imagine Figure Skater (by the developer of Princess Debut) and Imagine Teacher are respectable and fun, many of the others Imagine are absolutely terrible shovelware--tread carefully.
If u have to go the licensed game route, and given that she is 9, you may need to, High School the Musical Making the Cut (the first game) ain't so bad for an Elite Beat Agents clone, using a license she would like. Avoid the 2nd game like the plague (an awful minigame compilation), though the 3rd one is not too bad. Still the first HStM has fun rhythm action for the younger set, and shloads of unlockables with dress-up -- Wombat would like it. The Cheetah Girls Passport to Stardom is another respectable EBA clone for kids -- Disney is getting the EBA clone thing right. Avoid the Looney Tunes EBA clone though. If u think she can live without HStM, just get her EBA.
MySims and MySims Kingdom are okay, but u would be better getting her Animal Crossing.
Tinkerbell would not past muster with you, but she will love it.
For a puzzle game, check out Meteos Disney or Prism.
Spore Creatures is fun.
Avoid anything American Girl. THQ is not worthy of the license. The games are just not fleshed out and have serious quality control issues--like fast scrolling text that can't be re-read.
