I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
Co. Kerry rcds aren't in this database yet. Suggest you wait until they are. This may take some time, so be patient.
For Mary Doyle B 1863 (exact) somewhere in Ireland with the father's forename unknown, I found 33 rcds. Unless you have an exact DOB, parents' names, or a placename, you won't be able to eliminate the false positives and choose the correct, if any, rcd.
For Michael Fogarty's military service, he fought in the Indian wars - an exciting and dangerous period in history. You should be proud. You can get a copy of his service rcd at:
National Personnel Records Center Military Personnel Records 9700 Page Avenue St. Louis, MO 63132-5100
Google the name to get its website. Download an info request form. Complete it. Mail the form with requisite payment to the address indicated.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.