Dempsey ancestors

Good Morning,

I have been tracing my ancestory from Winnipeg, Manitoba Canada to New Brunswick, Canada to Ireland.

MYggg grandfather married in the Diocese of Cork and Ross 1820. Thomas Dempsey and Anne Sutton.

They had a baby 1821,  William.  I believe they had another baby...no record yet  or perhaps she had a baby while crossing to Newfoundland, Canada 1825.

I am anxious to connect their parents and where in cork.  The family name orginates from Offaly (King's county) but i know they needed to make their way to water in order to cross the ocean.  I am searching to make those connections.

Looking forward to any suggestion or assistance you may offer.

Julia