Yes. Lots of breastfed babies dirty a diaper every time (or most times) they eat for the first few weeks, or even months. This is totally normal and usually just means your baby is getting plenty to eat. You'll need to seriously stock up on diapers, but otherwise there is no cause for concern. If baby is having excessive (12 to16 per day), watery, stinky stools, call the doc — this may be diarrhea.