I've been researching my Baird line in Canada. The earliest ancestor I have been able to prove to my satisfaction has been Thomas Baird (b.1822, Amherst) the connection past Thomas to his father Samuel Baird (b.1785, Ireland) is circumstantial but compelling.
The sources I used to come to this conclusion are excerpts from the family bible of Jean Francis Baird, found in the family files of the Cumberland County Museum and Archives 150 Church St. Amherst, Nova Scotia; and a Land Transfer found at the Registry of Deeds Office (9 Havelock Street, Amherst, N.S.) Land Registration Book ‘U’ Pg 91.
I find it interesting that your Cornelius Baird and Sarah Moore are referenced as living in Ireland circa 1780, assuming that these are their child bearing years; it places my Samuel Baird within their timeline.
I have a hypothesis that Samuel Baird with his wife Ann Dickson immigrated to Canada between 1816 and 1822; likely late in 1816. Samuel Baird (1785) had a son who he also names Samuel (b.Dec. 1815, Ireland) as found in the 1901 Census of Canada, if Samuel (1815) was born in Ireland and Thomas (1822) was born in Amherst then the family would have crossed between these two dates.
Is any of this consistent with your research?