Not only are birth-dates in censuses 'variable', but, as we see, so are arrival dates. the Barker's were a pre-Loyalist family in Maugerville in what is now Sunbury Co., NB. Some went to York Co. See:
http://www.rootsweb.ancestry.com/~nbsunbur/marr07.htm
for some early marriages and:
http://www.rootsweb.ancestry.com/~nbyork/church/fton-wes-chr...
for some baptisms especially in Kingsclear Parish. The cemetery at:
http://www.rootsweb.ancestry.com/~nbyork/cem/PrWmCom.htm
suggests the Barker's were in the area fairly early; such as Thomas Barker (ca. 1777-1SEP1853).
These may be another Barker family as at:
http://mynewbrunswick.ca/barkers-point-bridge/
It is stated that Lt. Thomas Barker was a Loyalist. Since the Loyalists arrived in 1783, mentioned the pre-Loyalist, Jacob Barker, confuses the matter.
I can find no clear genealogy on either family at the moment, just a lot of Internet fluff. Maybe I can get back to this, but the Barker's are well worth pursuing.

Thomas.