There is no information about location.
Try searching "Carroll Ballydorgan" in google. I am not sure its the same family but worth a look.
Full address is Ballydorgan, Fermoy, County Cork, Ireland.
One of the hits is to this link:http://titheapplotmentbooks.nationalarchives.ie/search/tab/r...
There is a John Carroll and Ellen Carroll listed. If it is the family then John would be his father as this census was taken in 1824.