Hi Graebah, I quickly thought straight forward, but I checked both Irish Census b1901 and 1911 and there is a James, a carpenter, son of William John Edgar and Agnes Jane Edgar nee?

B. abt 1859, at Ballyboley. They married about 1875 There are 11 children living in 1911 [Greyabbey is spelt Greyabby and Grey Abbey.] The census doesn’t mention his 2nd name Dornan If he had an older brother William, he and two others are not listed in Ballyboley census. I don’t think they are mentioned in the birth and marriage indexs of
www.ancestryireland.com . However family search says your Agnes in Ballyboley is Agnes Dornan, the first child was David b 15 July 1879
William might be born since 1880 onwards, he must have left the family another brother is Alex is a Blacksmith at the age of 13 in 1901. I couldn’t find a birth
Ballyboley is a townland surrounding part of the eastern side of the Mount Stewart Estate. I wondered if he was employed by the Esatae and therfor more details might be found.
Ros Davies has a whole page devoted to Edgars on her website .
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/SURNAMES/E/Edgar.htm She has:-
William John EDGAR Down regd. Downpatrick; son of Matthew Edgar ; married Elizabeth Doran 23 Apr 1867 CR There are about 6 Dorans mentioned inc Dorrian etc, but no Dornan.
Living or visiting Canada, try the free index of migrants on
www.findmypast.co.uk/passengerListPersonSearchStart.actiontry birth years as 1891 plus or minus 1 year There are several possible listings
So not enough information, over to others to help your quest
Good luck JimG