I know that 赤ん坊 and 赤ちゃん are used frequently to refer to a baby but it would seem that 幼子 could also refer to a baby or an infant. In my dictionary it was even marked as "common". Now, I searched the word on google.jp and what came up on images were most definitely not babies (or at least, not any cute babies). Is this word just not used anymore?
幼子 sounds a little old, and we don't use this word in daily conversation. (not so old as we can't understand the meaning.) It also sounds formal, so it is sometimes used in essays or titles of books.
Instead of 幼子, we often use 幼児(youji, same as 幼子) or 乳児(nyuuji, a breast-fed baby). They sound more formal than 赤ん坊 or 赤ちゃん.