Hi - if they are your family how far back do you have them on US censuses, US birth/marriage/death records, etc? Have you looked for their arrival on the Ellis Island website? Some Irish alternatively came into Canada and "sneaked" across the border.
Biggest problem with this surname (one of my 2x grt grandfather's brothers married a Doherty in Nova Scotia) is the variety of spellings you will come across because of the pronunciation: Dockerty, Daugherty, Dougherty, etc. I have even found Dehorty.
Good luck - I will try to spend some time on this later.
Nick