I'm assuming you're using a digital camera. Outdoor shots work best... no flash and much less lag. Indoors, it's very difficult not to use a flash because the longer exposure time of a natural light shot will cause the subject to blur if there is any movement at all -- even with a tripod. An external flash (if you have a DSLR) can help with this. It will still be a bright flash, but it will not be so direct in the baby's face. Catching the moment when the child is not looking directly at the camera will prevent a direct flash in the eyes. You'll get a less startled look that way too. If you can anticipate a pause in the child's movements and snap the picture then, it will turn out best.
If you want to practice before exhausting yourself and frustrating the child, take pictures of your pets. They also move quickly and don't like the bright flash, so you can figure out what will work best with your camera.