The song doesn't say the pregnancy only lasted six months, but that the man came back when she was six month's pregnant. The version sung by the Waterson's is clearer in that respect as it actually says "Young man, I fear that I am with child by thee" - clearly pregnant.

Version posted by the OP is a little more ambiguous, but one line says "Perhaps you may have a child by me" implying (to me at least) that she has not yet had the baby, not that the pregnancy is unnaturally short.

While these days a child born at 6 months has a good chance of survival (my 2nd daughter was born at 28 weeks and is well and truly alive 34 years later) in times gone by a child born that early would almost certainly have died soon after birth if it was not stillborn anyway.