Book the infant ticket along with the parents.

Under no circumstances should you attempt to do it at the airport. That's only relevant advice for US domestic itineraries where the lap infant is free and guaranteed. Internationally, you pay 10% of the adult fare, but only with BA Avios will they charge you Avios instead.

As has already been mentioned, just add the child's likely name and make up a birthdate for 2023 so the child will be clearly under 2 on the date of travel. Later on you can kick that member out of your Household Account and add a new account with the child's proper name and birthdate.

P.S. You are very brave to travel with 2 lap infants