Catharine Moffitt/Moffatt

I am trying to find a birth record and parentage for one Catharine "Kate" Moffatt, probably born in Ahamlish, 1885 or 1886.  Unfortunately, there are a lot of gaps in this woman's history.  The only thing I know for certain is that she was in the US by 1907.  Per DNA testing, it seems as though she should fit into the family of Henry Moffitt and Catharine Healy of Lislary, probably as a grandchild.  I have extensive material on three of the Moffitt sons, but less data on two others - John and Michael - per family records and Ahamlish sacramental records up to 1880.  Does anyone have easy access to civil birth records?  Or any other suggestions? 

Thanks in advance!