Did not find any Dougherty's in the Griffith Valuation (census substitute) of 1862 might be spelling.
However, there are 9 Dogherty's in various parishes
There were 34 McGuire's in Fermanagh at this time. 23 are in Enniskillen. www.askaboutireland.ie
Depending on whether Margaret has older brother and sister, I don't imagine his parents would be listed in 1862, grandparents perhaps.www.familysearch.org
Margaret Dogherty registered birth 5 November, 1877 Fermanagh Fa: Patrick Dogherty
Mo: Margaret Mcgoldrich is the date you have her birth day, there might also be a parish baptism date as well.
There are two more 1877 but no parents names attached and a search with two parents you have given turned up no children that I could find.www.census.nationalarchives.ie
1901 & 1911 census if still in Ireland at this time. This site is spelling specific, I wasn't able to find either Patrick or Margaret
There is 1 Dougherty in the Fermanagh telephone book for Enniskillen, has a complete mailing address and postal code - the UK/Northern Ireland phone book
Hope someone comes along who knows the family.