That camera has two setting for the flash.
Normal and Red-Eye.
The Red-Eye setting is to try to reduce red-eye in photos of people. It flashes a light just before the flash goes off. This is supposed to cause the iris of the eyes to close down just before the photo is taken, thereby reducing red-eye.
If your camera is set for Red-Eye flash, that flash of light is causing your daughter to blink.
Set your camera to normal flash.
Help! i am using my first digital camera, and for some reason, I can't get a picture of my teenage daughter with her eyes open! i can get pics of other people, but not her! Is this a problem with this specific camera or am i doing something wrong? any solutions?