No! You have a golden opportunity to help her develop her ear and hone her own good musical taste. Please, don't encourage her to listen to Katy Perry or other shrieking tarts. There is no redeeming value--either in terms of musicality or content-- to the over-produced, hyper-sexualized tweenie-bopper genre. Let her be a trendsetter by developing her own unique style. At that age, kids listen to what their parents like and will be receptive to new sounds if a friend recommends them.

Get that girl some Miles Davis, Frank Sinatra, Foo Fighters, Dream Theater, Audioslave, Piano Guys, Pentatonix, Yo-Yo Ma, Carlos Santana, Tiesto, AC/DC, etc. Sample widely across genres. Have fun!

What is to give light must endure burning.