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I located the baptismal record for Catherine (see below) and she was baptized on February 9th 1844 in Ogonnelloe. Thady and Timothy were the same name. Here is a link to the parish register where baptismal records start in 1832 but marriages start in 1857. Let me do some additional digging.
First name(s)CatherineLast nameMulcahyBirth year-Baptism year1844Baptism date09 Feb 1844ParishOgonnelloeDioceseKillaloeCountyClareCountryIrelandFather's first name(s)ThadyFather's last nameMulcahyMother's first name(s)MaryMother's last nameCostelloeRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000634768#page/1/mode/1upRegisterBaptism