Depends, there are two terms:
Neugeborene = newborn. In German and Dutch the term is used to indicate a child younger than four months.
Säugling, or literally 'suckling'. In German and Dutch, it indicates a child younger than one year.
After that a child isn't considered to be a baby anymore, and is seen as a tot/toddler.
From how I have understood this so far, technically "Baby" is gender neutral, that is "das Baby". einen is used for "der" - or male direct objects, and ein is used for "das". It really does not matter what the sex of the baby actually is in this case - any more than "das Kind" - which is just child.
I hope that makes sense