Hi....
Just checked out
www.rootsireland.ie and these are the births that came up for an Ann Weir b.1818-1826 in Ireland but none in Dublin
View Church Baptism Weir Anne Mary 1823 Co. Kildare
View Church Baptism Wier Anne 1824 Co. Westmeath
View Church Baptism Wyre Anne 1824 Co. Louth
View Church Baptism Weir Anne Jane 1826 Co. Sligo
View Church Baptism Wyre Anne 1826 Co. Westmeath
View Church Baptism Wyre Anne 1826 Co. Offaly
View Church Baptism Wyre Anne 1818 Co. Roscommon
Her parents names would have been on her marriage record to James Jones
Hope this helps,
Annie