The townland Breagh has been mentioned.
In Armagh there seem to be three with this name
49950 Breagh 240 Drumcree Oneilland West Lurgan Armagh
49951 Breagh 257 Seagoe Oneilland East Lurgan Armagh
49952 Breagh 355 Tartaraghan Oneilland West Lurgan Armagh
from
https://www.swilson.info/db/townlanddbs.phpNB The third is worded like the mysterious 1851 census?
I have had a look on Griffiths 1864 for the occupants under the places tab and there are three Breaghs in Co Armagh entered - Drumcree, Tataraghan and Seagoe
http://www.rootschat.com/links/01sn9/In Seagoe there is a James Kerr, no Hamills. JK leases a house from Anne Jennett.
In Tataraghan there is a Patrick Hamill, Felix Hamill, John Hamill and Daniel Hamill
In Drumcree there are no Hamills or Kerrs/Carrs but there is an Edward McCann leasing a house & garden from a Robert Kingsborough
I think it could be worthwhile to do some lateral searching to find out all you can about Felix, John and Daniel Hamill.