If you want to register the baby with an email address you already have already used on a BAC account the online system won't work. You will need to call to set their account up using the existing email.
Also worth setting up a third party authorisation for yourself on their account at the same time so you don't have "we can only speak to the account holder" issues in the future. Third party authority on a BAC account has made things so much easier many times for me especially when a family member has a IROPS issue etc whilst travelling in another country as I can sort out the issue for them from the UK (appreciate the baby won't be travelling solo for a while but the years pass very quickly).