Hello Janice,
apologies for the delay in replying to your message.
You have a lot of good information so it should be possible to find Anne's baptism record.
You say she was born circa 1832 and died in 1905 so she should be in the 1901 census - the only older Ann Grimes I could find lived in house 2 in Castledown (Heathstown, Westmeath).
I can find a Daniel Duigan in the Griffith's Valuation living in Derrylahan, Killoughy, Offaly so this is possibly her birthplace.
My suggestion would be that you contact the Offaly genealogy centre as they offer a first search for just ?10 and your information is very specific.
The Irish Midlands (Counties Laois & Offaly) Ancestry service can be contacted here - please let them know we sent you!:
http://www.irishmidlandsancestry.com/content/contact/contact_details.htm
info@offalyhistory.com / Telephone + 353 (0)57 9321421.
Let's hope something turns up
regards
Dolores O'Shea
IrelandXO - Co. Offaly