Baby's father name has to be corrected in his passport to read the correct name of his father Irrespective of any case or situation or visa. Because, this is how your baby will be identified in India or International.

Yes absolutely It has to be rectified prior to applying your baby's visa in Qatar. You may ask your wife to approach the regional passport office from where his passport was issued and get it corrected by producing required/appropriate documents like his birth certificate.