I was able to book my ticket with the infant in one shot. The one catch was I needed the full number of avios required for the booking.
Just go to the award search and add the infant to the adult and the rest is pretty much the same purchase journey. I do not recall the exact total, but it was roughly an additional 10% in avios.

The other way to do it is to search for the inventory on BA and transfer avios to BA, although this is a bit messy in my opinion