That record from the CD was extracted from a set of films of Irish civil registration records that are available through the Mormon Family History Library. Had you already seen that record before? Have you found similar extractions of birth records for other children of your William and Catherine, and if so, have you also looked at the records on film or ordered them from Ireland?
You mentioned a marriage for William Crotty and Catherine Ahern at Carrigtohill, Cork in 1858. Do you have a church record for that marriage? If not, what is the source of the marriage information? Do you have baptismal records for any of their children? Do you know of other children of William and Catherine? Did any of them come to the US? Any other known Crotty or Ahern relatives? Did they come to the US?