I just found a pretty good autosomal dna match to a descendant of Jane b 1833. I am descended from Eleanor b 1794. The match implies 4th or maybe 5th cousins. Of course our common ancestry could be other than Turnbull.
Eleanor and Jane had several things in common - The Roxburgshire/Northumberland border area and New Brunswick, Canada specifically the settlements of Harvey and Stanley which were connected to the New Brunswick Land Company. Eleanor m William Grieve and they immigrated in 1837. Jane with her father David immigrated about the same time.
The standard genealogy is Eleanor's parents were Patrick and Alice Turnbull and Jane's were David and Margaret Turnbull. I am wondering if Eleanor was David's 1st cousin.
On a related subject it looks like their lineages may be Haplogroup R1b - Lineage I on the Turnbull DNA Project http://www.worldfamilies.net/surnames/turnbull/results
. Also see Turnbull Family Tree by dianeturnbull1