We applied for PR while I was pregnant, and we had our medicals when I was about 35 weeks along. You do not need to have an x-ray if pregnant, which saves a bit of money. Pregnancy can affect some of the blood test results, for example raised cholesterol, so I recommend that you ensure the Dr who fills in the medical forms notes any irregularities and states clearly whether these are pregnancy related. In my case my cholesterol was high, but this caused no problem at all. Also, despite being pregnant the examining Dr is still supposed to work out your BMI and take a waist measurment. Again, make sure the Dr notes down how many weeks pregnant you are which these measuements are filled in. Unless you were very overweight before getting pregnant, there should be no problem. And again, if you ended up having a medical not long after birth, I would recommend asking the Dr to make a note of this on the form.
When you submit your application, do inform your case officer of your wifes pregnancy, and they will guide you with the required additional paperwork.
Once your baby is born, you will need to apply for a passport as soon as you can after getting the birth certificate. Once you have the passport your baby will be required to have a medical too. My baby had this done at about a month old before he's even got a red book (child health record), and the Dr only did the same things that would have been done with a 6 week check-up with a health visitor, so nothing to worry about. It took the doctor all of 10 minutes to check my son over. Unless your child was born with some major health problems or congenital defects, it is simply a case of sending off the babies completed medical forms to your case officer to have it added to your residency application, and pay any additional fee that might be due.