Hi Kathy, the presumption that Anna Maria Brady was not a Catholic makes the possibility of tracing her , while still fairly remote, at least it shortens the odds a bit. The reason I say this is that when one searches for people with the "Brady" surname in Meath in the 1901 Census one finds 602 persons, but 587 of them are Catholic, and only 15 are presumably Protestant of some denomination. and in the adjoining county Cavan, where her parents could possibly have also come from, the numbers are even more striking. There were 3,420 "Bradys" in Cavan but of those only 51 were Protestant. The "Morrison" surname of her mother is much less frequent, in the 1901 Census there were only 8 Morrisons in Meath, and 16 in Cavan.
THe reason I am mentioning these numbers is because the only way I can think of detecting Maria Brady is to look at the small number of locations that Brady or Morrison families were living in 1901 ( as listed in the 1901 Census) , ie only those . that gave their religion as Church of Ireland or Methodist or Presbyterian, identify what Church of Ireland Parish that they were in, then see if any of those Old Parish Registers survived the Destruction of the Public Records office during the War of Independence in 1922-23 Then look for Maria's Baptism Entry in and around 1837.
I live quite close to the Church Library where the surviving records are stored and if I get some free time over the next few weeks I could see what they have that fits the criteria I listed above.
However I think the odds are very slim,
Regards
Kevin (meath999)