The Quin parish registers are online through the Clare Library website. You can access them here: https://www.clarelibrary.ie/eolas/coclare/genealogy/genealog.htm
If you go to the above link and then scroll down to Civil parish, you will see Quin and Clooney (Bunratty) from the list. Either of those will bring you to the parish registers.
Moore was not a surname in Quin or Clooney at that time. Is it possible that the name may have referred to Queens County which is the former name of Laois County? If you have Margaret's mother's name, that would be helpful.
Let me know and I will try to help you.
All the best,
Jane