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You really need to know Bridget's parents names to confirm any baptismal records that can be located. I searched Roots Ireland (subscription site) and they did have the baptismal record below for a Bridget Quinn in Galway city. It is a good lead but you would need other information to confirm.
Also, did not find a baptismal record for Thomas Mantle in Cork city. www.irishgenealogy.ie (free site) has available records for churches in Cork city.
Let me know what questions you have.
Name:Bridget QuinDate of Birth:
Date of Baptism:22-Dec-1831Address:GalwayParish/District:ST. NICHOLAS COMBINED N&EGender:UnknownCountyCo. Galway
Father:Patt QuinMother:Judy CarmodyOccupation:?
Sponsor 1 /
Informant 1:Thomas Grogan Sponsor 2 /
Informant 2:Ellen Grogan