We did that for our baby. Traveled at 6 weeks old within Asia and 3 months to U.S.

For both trips, I needed to give them the infant detail in advance so I could obtain a bassinet seat. On some airlines, they won't pre-assign you bassinet seats unless you were traveling with an infant. It is no problem for them to create an infant booking without Date of Birth or name yet. At least on CX and SQ they were able to do it and I called after the birth to give them the details.