Aghaderg RC’s parish records only start in 1816 so Mary has scraped in. If it’s the right family and her siblings were all older than her then there won’t be a record of their baptisms. (Nor of the parents marriage). It also looks as though Hannah’s age in the 1851 census may be out by a few years. Not unusual though.
Here’s a link to the baptism entry (30th November 1816):
Sponsors were Hugh Grant & Matthew Graham. No townland (address).
I have attached the tithe applotment records for Aghaderg parish in 1828. The tithes were a tax on land so these records list farmers. They don’t list labourers, servants etc and others without land (including obviously folk living in towns or villages). Hugh isn’t listed so we can probably assume he was a labourer rather than a farmer. However there are O’Hares farming there and there are Grahams. (sponsor at the baptism). I notice both names in Ballintaggart. Might be a coincidence or it might be a hint as to where your family lived.
Griffiths Valuation for 1863 lists a William O’Hare in a labourers cottage in Ballintaggart. His was the only O’Hare household in the townland then.
Your family had evidently left Ireland by 1850. There are very few records in Ireland prior to that they might be in. A labourer and his family could mostly live out their lives below officialdom’s radar. There were censuses 1821 – 1841 but as you will know, save for some fragments, they were destroyed. I can’t really point to any likely records that will tell you much more about this Aghaderg family.