I checked www.rootsireland.ie/ (a subscription site) for a birth/baptism of John Brennan 1814 & I'm afraid there were 14 records but none from Cork & none in November.
The only November record from Cork was Nov 24th 1810 DONOUGHMORE R C Parish parents Dennis Brennan & Ellen Cogan.
There are a couple of possibilities on a free site www.irishgenealogy.ie/ in the church records section from Cork & Ross parish:
There are various spellings of Brennan in the 1810 - 1820 range including 1 in May1814 parents Daniel Brennan & Eliza McCormack.
http://Name JOHN BRENAN Date of Birth N/R N/R N/R Address N/R Father DANIEL BRENAN Mother ELIZA MCCORMACK Further details in the record Sponsor 1 JAMES KAVANAGH Sponsor 2 MARY CULLEN Recorded Parochial Area SOUTH PARISH, CORK (ST. FINBAR'S, CHRIST CHURCH, ST. NICHOLAS, ST. JOHN OF JERUSALEM)