Have you made any progress yet on finding your Dorans forebears? The earliest family I could find in Kilmarnock is the family of Patrick DORRAN which is in the 1841 Census http://freecen.rootsweb.com/cgi/search.pl
. I have also located his death record in Kilmarnock in 1877. There are other members of the family listed in the Census, among them a Hugh and a David, probably brothers of Patrick. This is very probably the family you are looking for, all coming from Ireland to Kilmarnock before 1841.