You now see that some part of this family were still in Ireland in 36/37, you would have to try and search from then to perhaps when they immigrated, if they did.
Origins shows that Anthony Whittaker, James, William, Joseph & Bridget, Michael leased lands from lords in Ballyphilip, Birr, Clonbullogue, Kilcoursey and that a Harriet Whittaker leased out land in Edenderry. These are places to try and see at what time they may have moved from there, if they did.
If I get any more info I will forward same.
Regards,
Jack