Another for Team Human (I enjoyed it but thought that it started out deconstructing and criticizing certain aspects of the genre, but then ending up feeling more like it was criticizing people who criticized, but that may just be me and I doubt a 13 year old will care) and LJ Smith. I'd start her with Secret Circle and Nightworld too. I'm VERY partial to The Forbidden Game, too.
Cassandra Clare's The Mortal Instruments books, while having their fair share of problems, will probably appeal to her in a similar fashion as Twilight, and are generally less iffy. The heroine gets to take a more active role in the superheroing early on, her mother ends up central to the plot, and it has some female friendships, though they (sadly) take a while to get going. They're adapting the series for movies now, so it's possible its already starting to cross her path anyway.
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Cassandra Clare's The Mortal Instruments books, while having their fair share of problems, will probably appeal to her in a similar fashion as Twilight, and are generally less iffy. The heroine gets to take a more active role in the superheroing early on, her mother ends up central to the plot, and it has some female friendships, though they (sadly) take a while to get going. They're adapting the series for movies now, so it's possible its already starting to cross her path anyway.