I don't know about Singstar on the Wii. And I'm not sure if girls your daughter's age would be into it, but Beatles Rock Band is great for singing, as it allows up to a three-part harmony depending on the song. They've done a great job parsing the Beatles tunes to allow you to perform the songs with some semblance to the actual recordings. The original release gives you a great library, but they've been putting up more tracks over time that you can purchase for $2 each (I think). I imagine they're planning on putting the entire Beatles library up eventually, if they haven't finished doing that already.
Here's an example of what I'm talking about
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Of course, Rock Band is a full-band game with guitars, drums, and vocals. But I thought I'd point out the vocal aspect, as I'm sure you could get a lot out of the game with a group by just focusing on the songs with multiple vocal parts in that Beatles style. The instruments would be an added bonus in that case.