If she's anything like my 9 year old niece she will want something which can take a knock or two.

My niece has been using my GX-20 dSLR and producing some great shots. But that is hardly compact. However, it amazed me how quickly she got to grips with the basics, so she should be able to handle a compact no sweat.

What is the budget? May be something like this? or this

I'd go for a branded camera and these Olympus look quite substantial (I also remembered the TV advert).