http://www.dpreview.com/ tests cameras, the "in-depth reviews" includes reaction time, in the "timing" section. Look at the time lag for the different actions.
You didn't say what you (she) want in a camera. Tiny shirt-pocket size, wide zoom range, interchangeable lenses, etc?
You can get a decent, easily pocketable, 5MP camera from a major brand for a few hundred dollars now. Or the same in an older model for <$200. But if you have to have very short lags for full press of shutter button and taking of the picture, like <0.1 sec, that moves you to more expensive models.
In the meantime, what causes most of the lag is for the camera to autofocus and set exposure. Usually, if you press the shutter button halfway, the camera will set and hold focus and exposure, then when the moment arrives, you press the shutter button the rest of the way, and the camera will take the picture in <0.1 sec. (In the dpreview site's reviews, this is called "half-press to full-press" lag.) So you can get around most of the lag.