I used to do this for a living at Gamestop—recommending games all day long. I’d like to know more about her, if that’s possible. What kind of personality does she have? What are her favorite movies, books, or TV shows? There’s no set rule for what kind of games girls like.
I am a DS fanatic, and I play games of all types, so I’ll give some suggestions anyway.
Trace Memory, which was suggested above, is a great adventure game, but your daughter would have to be interested in a sort sad, bleak storyline and old-school Myst-style gameplay.
Animal Crossing: Wild World is almost a necessary purchase for any DS owner. Anyone, girl or boy, can get drawn into the very strange, cute world that your little avatar lives in. Collecting items, celebrating funny holidays (ACORN FESTIVAL!), and meeting strange animal neighbors.
Phoenix Wright is a story-driven game series in a fictional future where solving murders is done by lawyers, and anything goes in a courtroom. There are three Phoenix Wright games (Ace Attorney, Justice for All, and Trials and Tribulations), and one Apollo Justice game (same game, new protagonist), and more on the way. I love these games with all my heart. They’re funny, cute, engaging, and I never get tired of playing them. But she has to be into really dialogue-heavy adventure games.
Professor Layton and the Curious Village is a really complex game with beautiful animated cutscenes that revolves around solving brainteasers to advance the story. It also has the option of downloading new brainteasers and bonus puzzles. Highly recommended, since it’s both educational (lots of math and logic puzzles), and really fun.
Wario Ware Touch! and any Wario Ware, Inc. Gameboy games. These are amazing mini-game challenges that will keep her busy for hours. These games are an automatic purchase for me and I haven’t been disappointed yet. They have silly things like a booger-picking mini-game and a bunch of mini-games based around blowing into the microphone.
Cooking Mama games might also be fun. Similar to Wario Ware, these are all mini-games that create a larger recipe. Without the presence of Educated Mama or Executive Mama, the games are a little sexist, but they’re so damn cute that I just don’t care.
There are plenty more games, but like I said, I’d like to know more about your daughter first. The games I suggested are universally appealing, so they’re a good place to start.