Welcome to Ireland Reaching Out!
The expert session was conducted on the Ireland Family History FB page but you are welcome here nonetheless!
Firstly there won't be a birth record for Eliza as she was born prior to 1864 when civil registration was introduced in Ireland. I couldn't locate a marriage record for Jane and William and the only baptism I could find for children born to this couple was for a John Minnitt who was baptised on 16 December 1827. This record gives his birth date as 14 September 1827. The family lived on Lower Arran Street in Dublin and he was baptised in St. Mary's Church of Ireland parish. Sponsors to the baptism were not named. You can see the digitised original here:
Do you think Elizabeth could have married in the US?