Honestly, forget about "girl" games. When I was her age I would have been pretty pissed to get a "girl" game like Barbie's Horse Adventure or some crap.
First of all, unless she said she has a Nintendo 3DS, make sure you get a a DS game, NOT A 3DS game. A 3DS can play a regular DS game, but a DS canNOT play a 3DS game. So if she did not specify, you should probably err on the side of caution. It would suck to give her a game she can't play!
Here are my game recommendations:
* Animal Crossing. There are several to choose from, including New Leaf and Wide World. These games are life simulators and are lots of fun! You basically play a little character who runs around town making friends with all the animal inhabitants and doing things like fishing, bug catching, and decorating your home.
* Harvest Moon. Titles include Harvest Moon DS, Harvest Moon DS Cute (where the player controls a female protagonist), Island of Happiness, and A Tale of Two Towns. Similar to Animal Crossing, with more focus on farming. You make friends, raise animal and crops, fish, and so forth. In most of the games you find a partner to marry as you go through the game trying to save the Harvest Goddess.
* Super Scribblenauts. This game is so so fun. It's an interesting puzzle game. You get plopped into a puzzle and must figure out how to solve it. You write a word on a notepad, and whatever you have written will appear! (For example: The puzzle might be, "Help Santa deliver his presents!" And you could write "sleigh", "flying reindeer", and "chimney" and they would appear. Or you can get creative and replace the reindeer with flying dinosaurs, or a jetpack.
* Nintendogs. These games are about taking care of a cute virtual puppy. Think 2013 Tamagotchi. i haven't played this game but it's very popular and seems well-like with younger preteen kids.
* Tetris DS: A classic.
* Legend of Zelda: Spirit Tracks
* Pokemon Heart Gold or Soul Silver. Kids go fucking nuts over Pokemon. Also so do I. Pokemon games rule.
* New Super Mario Bros. Or anything with Mario in the title. Seriously, you CANNOT go wrong with a Mario game. Or Donkey Kong, or Kirby, now that I think about it.
All the games I listed above are low on violence and should be appropriate for a little girl! They're all fun enough for a girly-girl without the off-putting Princess formula that some girls HATE. Good luck, and you're doing a good thing!