What's the budget?
If she's really into it and learning photography from the inside out, I'd suggest picking up a used dslr and a 50mm lens.
If it's just for random snapshots then a point-and-shoot would be fine. Many times blurry pictures are from low-light and auto settings or camera shake, which is a problem when you zoom in for closeups. Even the inside of your house would be considered low-light. Just an FYI.
That Canon SD 1200 IS would be a GREAT choice if you want to avoid blurry...because of the image stabilization. It's what I would get if I were in the market for a pocket camera in that price-range (actually fantasizing here LOL) or the one right above it, which is about $200.
Unfortunately I think you'd be hard pressed to find better reviews for a compact camera in this price-range. The propencity to have issues with digital noise in low-light, etc. is just the nature of the beast.
