The baby is a Canadian citizen and doesn't actually qualify for an eTA. People have gotten them for their kids by not declaring their child's Canadian citizenship in the eTA application but that is actually lying.Sorry another question, if we just do the passport when we are there. Do we need to get baby a ETA visa to enter ?
I would advise you to get the passport so that the child has proof of citizenship when you come to Canada. The Certificate generally takes many months to process.