Unfortunately, there are six civil parishes in Ireland named Stradbally (in Irish, An tSraidbhaile, meaning "the street town"), and ten townlands with that name. However, the townlands are grouped together in most cases, with several being in the same parish in each case, so that actually narrows down the number of places to search. Here's a link to a list showing them all: https://www.townlands.ie/search/?q=Stradbally ; At that site, you have links to more info about each of the parishes and townlands.
Since you have an approximate year of birth, you could check the parish registers for each relevant parish in a range of several years around 1844, looking for your Elizabeth Moore. The year should normally be taken as an estimate, since people were often unsure exactly when they were born, but that was the year before the Great Famine so it's one year that people might actually have remembered well.
I notice that four of the Stradbally townlands (designated North, South, East and West) are all in the civil parish of Stradbally in Galway, and also all in the Catholic parish of Oranmore (the Catholic parishes and the civil parishes do not always have the same names, or exactly the same boundaries), so you might start there. The parish records for Oranmore are available (free) online at thiis link, and they go back to 1833, so if Elizabeth was born in any of those four townlands, then you should be able to find her: https://registers.nli.ie/parishes/0634
If you have no luck in Galway, that site has an interactive map which allows you to move on to other locations. The two Stradbally townlands in the civil parish of Stradbally in Limerick are both in the Catholic parish of Castleconnell, and the parish records for Castleconnell are available here (going back to 1850): https://registers.nli.ie/parishes/0758
The two Stradbally townlands in the civil parish of Stradbally in Waterford are both in the Catholic parish of the same name (Stradbally), and the parish records for that parish are available here (going all the way back to 1805): https://registers.nli.ie/parishes/1093 ; Actually, since in this case the townland and parish have the same name, perhaps this would be the location to start with, but it's up to you.
By the way, all of those townlands are searchable on Google Earth, using just Stradbally and the county name, and that allows you to see what they look like today.
