Mooney was (and still is) a quite common surname, and based on the details on Griffith's Valuation (1850s/60s) present in most counties in Ireland. The top 5 locations at the time were
1. Dublin 163 (approx number of households)
2. Offaly 138
3. Antrim 126
4. Down 107
5. Meath 103
many other counties had significant numbers also..
Unless a surname is quite rare, a surname distribution would not usually be of much use in determining a birthplace...
Shane