It depends on your travel style :-)
If your dates are fixed by train tickets or specific events then you may as well pre-book all your nights. But if you have a car and a loose agenda, you could book as you go. You could book a few days ahead or just drive up to places you find along the way. The later approach is most flexible and potentially the most stressful. I have done it and gotten great rooms at a good price and other times had to drive further to find affordable lodging. But that was mostly in France and Italy, not in Ireland. Walk up booking while using public transportation is not something I would try.
The last few trips we left a block open which we planned and booked while on vacation. For our next trip in March-April, I only have the first night booked and will probably book the last three nights soon. The remainder depends on getting snow in the ski resorts, so we are doing snow dances and changing our itinerary with each storm. B-)
Enjoy the trip!