Patrick Dougherty, b. 1784 and James J. Dougherty, b. 1785  spelled their name without the "O"

The significance of such a distinction is that country Antrim was in the Protestant north of Ireland whereas County Mayo was in the Catholic part (Eire). The Dougherty's that came to Canada were Protestants - even though the grandfather of immigrant John J. Dougherty, b. 1825, was Patrick O'Dougherty b. 1750 - who spelled his name the Catholic way with an "O".

You might also note we marked County Donegal also since that part of Ireland is also famous for a large number of Doughertys coming from there. Many of the websites about the O'Dochartaigh clan refer to Donegal, rather than Mayo

County Antrim
"In the period before the 17th century, when the county was part of the territory of  the O'Neills, there was much migration from Scotland"
 scripts.ireland.com/ancestor/browse/counties/ulster/index_an.htm

".. owned by Conor Mac Gearóid Ó Dochartaigh, and although having a strong keep, it had no bawn at that time. It drew little attention from Docwra, chief of the English occupants in the South of Inishowen and in Derry. It was repaired by Hugh Boy O'Doherty in 1602 to act as a meeting point for the Spanish armada, who intended to land on Inch Island and use it as their base. 

In 1608, it was chosen by Sir Cahir Rua O'Dogherty, after his rift with the English, as a place to gather his supporters together before marching on Derry. It was burnt by the English, although the walls stood and it was repaired soon afterwards. It was leased to Henry Vaughan, who had come to Derry with Docwra. He lived in the castle with his family until the completion of the nearby house in 1718. It is said that the castle was demolished 
to build the house, although it is more likely that it was the bawn wall that was used, as none of the stones around the castle seem solid enough to have formed part of the bawn wall. 

The original castle had two storeys, with deep recesses and loophole slits. There were three periods of construction, with additions and adjustments being carried out with each period. The second period was concerned with the fortification of the castle in 1602, and the final period with Chichester's or Vaughan's repair in about 1908." 
from 
 www.iol.ie/~inishowen/inishowen/castles/crana.html

additional reference to the clann O'Doherty's Castle [Keep] 
at  http://www.dun-na-ngall.com/buncrana.html

notice the crest of Buncrana has a stag deer in the same leaping design as on the Ó Dochartaigh clan herald

If you go to this page you may read detailed info on the origins of the buncrana herald symbols in which specific reference is made to the Ó Dochartaigh clan 
 http://www.ngw.nl/int/ier/b/buncrana.htm

"Inishowen was the last Gaelic stronghold in the province of Ulster to come under British occupation in the 17th century. The cultures, traditions and language of the Gaels remained strong in the peninsula until the twentieth century. The Irish language was the everyday language of much of the peninsula until the late 1800s, especially in areas such as Clonmany, where there were still native speakers of the language until the mid 1900s." 
- says Michael Ó Nuadháin who built the page on Inishowen
 www.iol.ie/~inishowen/inishowen/index.html

- official O'Dochartaigh (Doherty) Clann Website
2005 O'Dochartaigh Clann Reunion