Hi - what else do you know about your great great grandmother ? There is a Miriam Parry born 1844 living in Llandygai, Caernarfonshire (this is the area we would call Mynydd Llandygai nowadays which is very close to Penrhyn Quarry, etc). She is a servant to a Davies family. This is the only mention of a Miriam Parry in the census' in this area in any of the census years. I've also checked the GRO but civil registration wasn't compulsory.
Do you know her husband, children, etc to see if you can get further back. The more information you can share the better.
Nesta