There is so much crap in our drinking water that I don't drink it myself and don't give it to Rosie. I have a distiller and distill our water at home and add back in some minerals myself. The same is said about humans drinking distilled but with minerals added and a decent diet you are getting those minerals elsewhere also. We have been drinking it only for over 6 months with no problems and I would be confident that water for infants has in it what it needs and should also be fine for our fur babies.
Here's something I did that I thought was interesting. Put the distilled or nursery water in one bowl and the tap or filtered in the other and watch which one the dog chooses.
Mine goes for the distilled every time.