Congrats on your precious baby. Though I did not read cards when my daughter was that young(I had not discovered them yet), I think it's common to be frazzled no matter what activities you attempt.
Study when the baby is sleeping, at night or naptime-unless you need sleep too- then do that. At least now there is youtube. You could even have some of that playing as you go about your day.
Later, when the baby is older, you can use Tarot together as a sort of play time, story telling thing. You'll be learning and practicing to some degree, and the baby will be getting a story
The main thing is to not get discouraged. Treat the tarot for now as your own private time and engage whenever you have a free moment. Just remember, it can be a slow process to learn for any of us, so just enjoy the journey...and don't miss out on a second of the baby's journey, either
Best of luck to you xoxox