I have started looking for Edward and Margaret's children in the Irish Family History Foundation records. Please bear in mind that their records are not yet complete, since only 19 of the 32 counties are presently online. You did not say if you have copies of any marriage certificates. I could not find any matching Cuddy/Burbage marriages. Perhaps they were married in Canada? I found the following baptisms a few years either way of 1843:
Action Source Surname First Name Year County
Church Baptism Cuddihy Michael 1838 Co. Kilkenny
Church Baptism Cudihy Michael 1839 Co. Kilkenny
Church Baptism Cuddy Michael 1840 Co. Roscommon
Church Baptism Cudihy Michael 1841 Co. Kilkenny
Church Baptism Cuddy Michael 1842 Co. Kilkenny
Church Baptism Cuddy Michael 1843 Co. Roscommon
Church Baptism Cuddy Michael 1843 Co. Kilkenny
Church Baptism Cuddihy Michael 1844 Co. Tipperary
Church Baptism Cuddy Michael 1844 Co. Tipperary
Church Baptism Cudy Michael 1845 Co. Roscommon
Church Baptism Cuddihy Michael 1846 Co. Tipperary
Church Baptism Cudihy Michael 1846 Co. Tipperary
Church Baptism Cudihy Michael 1846 Co. Kilkenny
Church Baptism Cuddihy Michael 1847 Co. Kilkenny
Church Baptism Cuddy Michael 1847 Co. Kilkenny
Church Baptism Cuddihy Michael 1848 Co. Tipperary
Church Baptism Cuddihy Michael 1849 Co. Kilkenny
Church Baptism Cuddihy Michael 1850 Co. Kilkenny
Church Baptism Cuddy Michael 1850 Co. Kilkenny
These are baptisms and births for Catherine Burbage. As you see, Burbage is a Longford/Leitrim name:
Action Source Surname First Name Year County
Church Baptism Burbage Catherine 1839 Co. Longford
Church Baptism Burbidge Catherine 1849 Co. Longford
Church Baptism Burbage Catherine 1853 Co. Leitrim
Church Baptism Burbage Catherine 1863 Co. Leitrim
Church Baptism Burbage Catherine 1865 Co. Leitrim
Civil Birth Burbage Catherine 1866 Co. Leitrim
I will now search for the others.
Marian
Manager