Hi Fred,
Well it's great to have a father's name BUT that still doesn't get us much closer to finding her.
Ann was born 1832, our civil registration only began in 1864.
So, find someone prior to 1864 you need to look for baptisms.
For that you need :
Father's Name
Mother's Christian AND Maiden Name
Parish & Townland that Ann was from.
THEN
You need to see if records for that parish still exist.
So, without all the extra information I'm afraid we can't help you over here in Ireland.
Again, you need to get together as much ACTUAL OFFICIAL PAPERWORK together for her if you really want to try and find her roots in Ireland.
You need to get the official marriage cert to see if there was possible family as witness' to her marriage, you also need to get her father's occupation from the official marriage cert.
You need to get her official death cert to see if there are any leads that way.
You need to get every census that she appeared on to see if any of them mention anywhere more specific than Dublin.
You need to get all her children's baptisms to see if any of her family members were Godparents.
You need to trawl through all the census that she was on to look at all her neighbours to see if any of them were family members.
So, as you can see, there is a lot of work that YOU need to do on her before trying to find her family in Ireland.
Best of Luck and please do get back to you when you have some concrete leads.
Tara