Dont use the pop-up flash! Bounce the flash off of something, or just set the flash so it only pop's a little bit, like fill flash.
Animals, babies and people who are drunk, well drinking, will almost always have devil eyes if the flash hits them directly. Their pupils wont dialate quick enough from the flash (Which is also why a police officer will shine his flashlight into your eyes when they ask "Have you been drinking?"
If you dont have an off camera flash to use, tape or rubberband a napkin around your pop-up flash and it should diffuse the flash enough to take care of it.
There are also a few little aftermarket items you can use to soften the flash, but even Dalantech uses a napking, and look at his results! Best I've ever seen!