The Lego camera looked good at first, but reviews are awful. Basically, it's just some lego-looking plastic around a 2005 cell phone camera. She would see right through that.
I immediately thought of the waterproof, ruggedized models, but they're all well over $200.
The fixed lens is a great suggestion, but I don't see any at this level.
Right now a Sony Cyber-Shot DSC-W620 looks like it may be leading the pack ($98 at Amazon).
Anyway, I'll keep looking. Still 22 big shopping days until Christmas!