Baptism is a Christian rite of admission and adoption, almost invariably with the use of water, into Christianity.
Baptism is an old practice came from ancient cultures including Hinduism and idol worshipers. It is claimed among Christians that Prophet John baptized Prophet Jesus but there is no authentic evidence available. We do not have any evidence that any prophet was ever baptized.
Islam does not allow acts which have no evidence.
You should not take any part in any worshiping practice which has no authentic evidence.
Muslim is not allowed to attend or take part in any non Muslim religious ceremony.
The child mentioned in your question is a Muslim because of his Muslim father. Islam says that any child who is born from Muslim father or Muslim mother, is a Muslim.
الولد يتبع أشرف الأبوين
There is no question of baptism ceremony for a Muslim child.