Most tattooists will not knowingly tattoo a pregnant or breastfeeding mother. This is for liability reasons on the tattoo artists part, but also to prevent any disease that might affect the growing baby, and to allow the mothers body time to heal.  It is suggested that mothers wait at least until 9-12 months after birth, when the child is no longer dependent solely on breastmilk before getting a tattoo.  Reputable tattoo artists will have a waiver for the client to sign that asks about pregnancy and breastfeeding.