Look at this way, Dude: If your daughter has any real talent and decides to pursue this for a living in some fashion, whether it's as a songwriter or sideman or a band or whatever, it makes more sense for her to walk into a room and play right handed.
If she's asked to sit in somewhere or sit in on a session or contribute to a song or whatever, she'll always need to have her left-handed instrument on her at all times. IMO, that's a major detriment.
And as I said earlier, guitar is easy. It's just shapes. I doubt she's out to be the next Yngwie Malmsteen. And make her take piano lessons as well. If you can play piano, you can virtually understand and play almost any instrument because it's laid out so simply that the music theory is natural.