Hi
I couldn't find any reference to a bar of that name in Wicklow. The bar may have its official name like the 'Dunlavin Inn' or some other similar name, which may have been owned by Mr or Mrs Doody and locally called 'Doodys'
You reference Dunlavin and I found the following 2007 newspaper tribute to an Eileen Doody of Dunlavin, there may be a connection.
https://www.independent.ie/regionals/wicklowpeople/news/family-pay-trib…