Who was Margaret Cotter Barnes

My great-great grandmother, Margaret Cotter (census' cite her varying birthdate 1821 - 1825) married John Haddock Barnes in abt 1843-1845. She was born in Canada, East which on later census' meant Ontario. Her parents came from either Ireland or Canada (varies on census')
How do I begin to search for her records when all I have are her US documents, (from NY to Ohio to Iowa to Omaha) but no leads or clues to specifically where in Canada she lived, where she married John Haddock Barnes (b 1825, Milton, NY) or who her parent were or where they were from.
Answers just lead to more questions...I hope to hear from you. Thanks, Loren