You can have it post birth. You having it doesn't automatically protect your child it just reduces the likelihood of them catching it - your partner should get it as well because realistically they are more likely to come into contact with it when your bub is little because you tend not to go out as much.

You don't have to have it but whooping cough is a truly terrible thing in little kiddies. As someone who has seen a tiny baby with it I would recommend that you did everything within your power to reduce the risk.