I was in Dublin once and was told you had to go to each parish to ask to look at the registers--and Dublin had over 300,000 people at the time of the famine. I figured it would take too much time--and maybe she wasn't actually born in Dublin. My grandmother, her granddaughter, was alive at the time and would have been delighted if I could have found something.
I was in Dublin once for my birthday, more or less passed out in a Queen Ann chair in the lobby of the hotel. I had a lot more fun in villages and towns (particularly Clonmel).
Given your ancestors comes from Dublin, you may be able to track down readily easily.
While I’m reluctant to state it here, but my surname is ‘Fitzpatrick’. One of only two ‘Fitz’ prefix surname to predate the Norman invasion. My ancestors come from near Cavan Town. There is some controversy about this, but in the original Gaelic, Mac Giolla Phádraig (anglicized ‘Fitzpatrick’), means sons of the servants of Saint Patrick.