A "sow's baby" is, according to slang dictionaries from the early 1800s, a pig, or sometimes a suckling pig. Why they felt the need to clarify this is unknown. More usefully, it was also slang for a sixpence, because it is half a shilling, and a shilling was often called a hog.
A "sow's baby" is, according to modern crossword dictionaries, a clue that probably means piglet.