I wouldn't and most places won't either. The tat itself won't hurt the baby but I've heard some awful stuff about how pron we pregnant women are to infection and I'm not 100% sure on the ink I'm sure there is a safe one if you can't not don't go to the cleanist place you can possibly think of and don't get one on your torso. I know how you feel I wanted one sooooooo bad with my first son lol
As a tattoo artist I will tell you. Your gonna be hard pressed to find an artist who will tattoo you. Pregnant woman have a higher rate of infection. It has nothing to do with the ink, we swell worse, the ink seeps worse which leads to premature aging which will give ur artist a bad name, and with the amount of hormones we have it's much easier for your body to go into a shock state.