The piano is just fine, doesn't sound too elementary, this rather simple way of accompanying works well with this song. I think I just detect a very slight irregularity of tempo within the first minute, piano seems to push forward a little in relation to your daughter, but not very noticeable. Great vocals, I wish "my" classical soloists could switch to this kind of pop singing style whenever it fits, but as they learned a different technique it's difficult to switch a button and sing differently...