Conlet:
I looked at Roots Ireland www.rootsireland.ie and found an 1816 baptismal record for a Mary Harty born to Michael and Mary in the Ballybricken/Bohermore RC parish. No surname was shown for the mother.Also found a Margaret born to the same parents in 1820 in Ballybricken and there were five other Harty children baptized between 1814-1834 to a Michael and Mary but I did not check the parish. This may be a different Harty family particularly since you have 1824 for her date of birth.
Roots is a pay site to view a transcription of a church record.
Many of the Co. Limerick parishes have records going back to 1820, however, a good number start later. There is always the possibility that your Mary was baptized in a church with later records.
I don't know if her father lived until 1850 but below are the five Michael Hartys listed in the 1850 Griffiths Evaluation head of household listing for Co. Limerick. (The townland is after Michael).
Roger McDonnell
GriffithHartyMichael GlenlaryBallingarryCo. Limerick
GriffithHartyMichael FanningstownFedamoreCo. Limerick
GriffithHartyMichael Knocklong EastKnocklongCo. Limerick
GriffithHartyMichael Mitchelstown-Down EastKnocklongCo. Limerick
GriffithHartyMichael GortacloonaKnockainyCo. Limerick