Some of these are before the marriage date you mentioned (is this detail verified?) although the date for Mary's birth matches exactly ... there might be another couple in Cork with the same names
some possible matches in the extracted births on Familysearch - looks like this family were in Cork City for at least some of them :
see:
Quirke/Sullivan searchUnfortunately none of these have page numbers which you can use to cross-reference the births with the civil BMD Index and register - but it might be possible to find a possible matches by name and year. The registration district on the BMD Index would be Cork (as in City and surrounds)
The extracted records include some of the civil births between 1864 and about 1880 - so would not include the younger children - Michael, Denis or Joseph.
Shane