For domestic US flights, you do not need a ticket to have a lap child, i.e. under 2 years old without an assigned seat. When you make your booking, just tell the airline that you'll be traveling with a lap infant. They will ask you for the name and age of the child when you check in; no birth certificate or other id required for a child who is obviously less than 2 although it can't hurt to carry one.

On the other hand, if you want a seat for the infant (presumably to install the car seat), you will need an infant ticket which generally costs 10-50% of the adult fare. I imagine that the airlines have a provision for issuing these in without a first name (i.e. Baby Smith) for as yet unborn children. You should, of course, book this at the same time as your tickets to ensure that a seat is available.

Hope this helps; have a wonderful trip!

Michael

p.s. please let's not restart the debate about the safety of lap infants in this thread when there are thousands of other threads on that topic to choose from.