Hi Christine
you have done exceptionally well to get as far back as you have with your research as you have as Irish records are poor before the 1850s. I do not think there is a volunteer in the area you are looking so I will try to give you some information.
My best shot is to try this site and search the names as it contains lists of various types for the period
see http://www.jbhall.freeservers.com/index.html and you will get a lot of hits for McGough and Mooney, Mooney in particular is a common enough name.
The Flax growers lists of 1796 give McGoughs in the Dowdalhillls area but you iwll have to cross reference to see if there are Mooneys in the same area which might indicate they came from there, it is a small area near Dundalk. There are Mooneys in Faughart but only 2 McGoughs on the list one in Collon about 20 miles away and I do not recognise the 2nd place, but not everyone is on the list only those growing flax.
A paid website is the https://www.irishtimes.com/ancestor/ and http://www.rootsireland.ie/ also pay but if you register you can do limited searches.
Other area you could search if in Ireland are land registry and the registry of wills but this assumes they were people of some wealth and standing. Dublin locations for look up.
In 1816 in the area there was social upheaval when Wildgoose Lodge was burned killing a number of people which resulted in the hanking of 9 others I think, some at least who were innocent, a synopsis is on the first website and a full book was published about two years ago. Fairly brutal too.
If you think there is anything else I can do let me know.
Regards
Pat
