The Bridget I gave you was the only one on www.familysearch.org
They recently updated the website.
If the death certificate said she dyed a few days after childbirth then you should take that as a given. There were many reasons, excessive bleeding, placenta previa, septicemia you name it. The name John Flynn would be the person reporting the death to the registration district as he was next of kin.
Few parish's have deaths recorded in the registers unlike
baptism and marriages but fortunately due to civil registration you were able to get this information.
On an old CD set from the Latter Day Saints:
Bridgeta (Latin) born 8 June 1830, Killukin
Nicholai Elwood/Honor Elwood
Brigidam 28 Aug. 1833 Laughlin
Thomas Elwood/Mariae Regan
Bridget 17 Jan 1839 Strokestown
Thomas Elwood & Maria Devany
Brididam 18 Oct 1839 Killucan & Ballinameen
Richardi Elwood/Eleanorae Collins
Brigidam 3 June 1846, Killucan & Ballinameen
Gulielmi Elwood/Marie Hanly
Brigidam 27 Sept 1857 Loughlynn
Joannis (John) Elwood/Catharinae Giblin
These are specifically from parish's that the records were saved from the 1922 fire at the Four Courts, Dublin.