If you are pregnant or nursing a child, everything that goes into your body also affects the baby. Everything from spicy food to drugs ends up in the placenta and your milk. When you get a tattoo (or a permanent makeup) you are taking the risk of possible allergic reactions that could potentially be passed on to your child. To protect unborn children and nursing infants, most studios have made it a policy not to perform tattoos or piercings on anyone pregnant or breastfeeding women.
During pregnancy your immune system is suppressed by autoregulating mechanism that supports a new life. Trauma created by tattoo can be enough to cause complications. Not to mention that if this is your first tattoo, you are unaware of the side effects that may occur for your specific situation. You may already be noticing how pregnancy changes your skin which becomes sensitive to new irritants. If your skin becomes irritated from a scented lotion how much more discomfort will you experience from dyes being injected into your dermis?
There are other factors that can negatively affect the outcome of a cosmetic tattoo for a pregnant or nursing mother. Hormones affect the growth and appearance of the skin, hair and nails, hormonal changes during pregnancy and the postpartum period which can bring out noticeable, sometimes permanent changes in appearance for some women. As far as the skin and tattooing goes, it may be more susceptible to pigment darkening (especially for those who experience melasma, the "mask of pregnancy") or perhaps more resistant to accepting the tattoo pigment. Some, of course, will be unaffected by their hormones just as they might have been spared all the other commons symptoms of pregnancy. You just never know