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.