I have a Kindle Paperwhite and while I suppose it could be used for the internet, it would take about 30 seconds of browsing before I threw it out the window because the "experimental browser" is so bad at internet. LOL at the thought of youtube or music videos on it.
So I wouldn't worry about that if you get her a Paperwhite?
I think the Kindle Fire has parental controls that allow the parents to set limits on the amount of time kids can spend doing different kinds of activities (browsing, playing games, etc). You could set it up to limit play time, then tell the parents how to change it if they want to.