City of Dublin records on www.irishgenealogy.ie
South Dublin and North Dublin have their own genealogy
offices but both belong to an Irish History Foundation
that has parish record.
I only found 1 counsel in Dublin County Griffith Valuation 1849:
Peter counsel, Parish of Taney, Townland of Ballinteer
Poor Law Union Dublin S. tenant of Mrs. Townsend
# 9b a house
There was also a County Louth,
Bartley Counsel Parish Clonkeen, Townland of Stormastown
3 County Wicklow Counsel's. John, Anne and a George
One thing that Irish families did was carry family names down through the generations, so look at her children's names for clues.
Mary probably married about age 20 so about 1851+
If they were Protesant there are marriage records from 1845-1862 (no matches for the surname Counsel) or if married in England try www.freebmd.org.uk
or if in Canada: Collections Canada
For Canadian passenger records you could trywww.theshipslist.com
Parish records are available on line for County Dublin South, Lough and Wicklow on a not for profit but fee paying Irish History Foundation. You just need name and a year and you have both. A birth record would have her mother's name, father's name and mother maiden name, place/parish and full date. You don't even need a county.