While I did not go back to school or study for a major licensing exam after having a baby, I can provide this advice. My view is that it is possible if you are very structured and process oriented and if you are diligent in getting your child on a regular schedule. There are several very good books out there that provide advice on this topic. One is the “Baby Whisperer.” There is another that I read but the name escapes me. The author is rather militant, but you can pick out what makes sense to you. You will have to plan to do nothing other than take care of your child, yourself, your house and study. You will also need the support of your spouse and should work out roles and responsibilities to assist your goal. If you have family close by you may want to enlist help from them as well. Depending on your situation, and if necessary, you may want to consider getting a sitter for a few hours a week so you can focus on studying.
Your view that the first 3-4 months are for the baby and recovery is right on. The 4th trimester as it is termed, requires pretty much full time self care and child care especially if you are nursing (which is a wonderful thing and I highly recommend it). Now, there is always the risk that you could have a difficult baby and that may slow you down, but again if you are diligent with going through the “pain” of training your baby and getting him/her on a regular schedule, life will be much easier. I also recommend that you really try to do this with your first child. It only gets more difficult with a second.
Congratulations and Best of luck!