First up - congratulations to OP! A very exciting time and good luck with it all.

I had exactly the same issue a year or so ago, looking to fly to Madrid. Wanted to book well in advance before baby was born. I made an Avios booking for BA just under the names of my wife and I. After the birth and with name duly conferred I called up again and added the baby to the booking with no problem at all. Only note is that I had to call Avios as the booking was through them, not BA, and they issued the relevant ticket. As the baby takes up no room and is on lap it's straight forward to add tickets.

Remember as well that those with infants can book seats 7 days in advance I think to ensure you all sit together as a family. Good luck!