You should buy them! Music is after all entertainment - so the best headphone is the one that brings the most enjoyment to the owner. It doesn't matter if they connect with the color, shape, or sound quality. The important thing it that they like it. What use is buying a great sounding headphone, if your daughter doesn't like the way it looks, and is less likely to wear it?
Beats have a bassy modern sound to them. They aren't the most accurate sounding - but that isn't the point of them anyway. Audiophiles get enjoyment out of owning the most accurate equipment, yet most recording studios use monitors like Yamaha NS10 that have an extremely uneven EQ. Ironically audiophiles with flat EQ headphones and speakers hear a sound that is drastically different to what the artist heard in the studio!
I've used lots of different studio monitors and headphones, and I like beats headphones for their fun, bassy sound.