I wouldn’t be able to meet you in August as I live too far away. However I can offer a little information about your search.
Statutory birth registration didn’t start in Ireland till 1864 so you won't find a birth certificate for Matilda. You might find her baptism but to do that we’d need to know her exact denomination. Do you know what that was? Looking at the 1901 census of Co. Armagh there were 174 people names Hanna. The majority were Church of Ireland or Presbyterian but there were also some Reformed Presbyterians, some Non Subscribing Presbyterians and some RC.
I noted 1 Matilda Hanna born c 1862 in Armagh City in the 1901 census. She was Presbyterian:
Looking at the PRONI catalogue of church records for the Keady area, the Church of Ireland in Keady has records from 1780, the Church of Ireland at Armaghbreague lost it’s early records in the 1922 fire in Dublin and has nothing before 1877; The Methodist has baptisms from 1815 (kept now at Armagh Methodist church, as the Keady Meeting House has closed); 1st Keady Presbyterian has records from 1838; 2nd Keady Presbyterian from 1855; Armaghbreague Presbyterian has baptisms from 1908 (earlier records seem to be missing); Tassagh Presbyterian has records from 1843 & Derrynoose RC has records from 1835.
The RC records are on-line on the nli site and the Methodist records are with the Methodist church in Armagh which means a visit there to look them up. The rest of the surviving records have been copied and are held in PRONI (the public record office) in Belfast where they can be viewed free.
If possible you should try and get your Matilda’s parents names from marriage or death certificates to ensure you locate the right family. You will see that there was what I assume was another Matilda of about the same age living in 1901, so you need to be sure of identifying the right family.
I searched the rootsireland site for Matilda born in Armagh c1858 but did not find one. However many of the church records are not on-line and so that doesn’t mean anything. PRONI is the place that holds most of the records you need to search. They are not on-line and a personal visit is required to view them.
If your Matilda did come from Keady it shouldn’t take more than an hour or so to check the records in PRONI. However if she came from somewhere else in Armagh then it’s a bit of a needle in a haystack.