...Note that Mary Elizabeth is showing there with the maiden name of Hudspith.
That note was from Georgina's death reg earlier. This looks like her birth:
DOUGHERTY, GEORGINA Mother's maiden name HUDSPITH
GRO Reference: 1857 J Quarter in HEXHAM Volume 10B Page 208
How about this for son Robert's birth?
DOUGHERTY, ROBERT Mother's maiden name HUDSPITH
GRO Reference: 1861 M Quarter in ROTHBURY Volume 10B Page 329
A possible entry in 1891 in Carlisle, St Mary Within, Cumberland:
Robert Docherty 30 mason's lab b. Alnwick, Northumberland
Margaret Docherty 28 b. Carlisle Cumberland
Robert Docherty 1 month b. Carlisle Cumberland
Alice Collins 1 niece b. Scotland...this would be Alice Agnes's daughter b. 1889 in Kirkcudbright
William Docherty 17, boarder, cattle driver b. Scotland....is this your William I wonder?
Possible death for him:
Robert J Docherty
Age 52 (born c. 1861)
Carlisle Cumberland
4th Qrt 1913
Vol 10b/pg 369
1901 family entry in Carlisle
www.familysearch.org/ark:/61903/1:1:XSVJ-ZWXMonica