It has nothing to do with infections or ink poisoning. Tattoos aren't recommended because your body can go into shock (without you even realizing it) during the tattoo. It all depends on you and your pain tolerance. I've had multiple small tattoos while pregnant in the past. If course I got permission from my doctor first. Just talk to your doctor and stick to small tattoos if you can handle it. Congrats :)
Tattoos are not considered safe during pregnancy due to the risk of infection