With so few days I would not try to get to Dingle by public transit, it will eat up too much of your time. Honestly, with the time you have I would pick Dublin and one other city to base in, and use guided day trips to see the sights. Otherwise, you will find yourself rushing from place to place, and you won’t get to see many sights due to the time spent getting from town to town. Getting to Killarney by train will eat up half of a day, then you would have a couple of days to do guided day trips ( Dingle, Gap of Dunloe, Ring of Kerry are some choices), then you would have to get back on a train to return to Dublin. Galway is closer to Dublin by train, and there are many guided day trips you could do from there, also (Cliffs of Moher/Burren, Connemara, Aran Islands). So, if you don’t have a car, and want to spend 2 or three days seeing sights in and around Dublin, then pick just one of either Killarney or Galway to spend the rest of your time in. Having done a three week trip using a train/bus pass I would be inclined to split my time between Dublin and Galway if I just had a week. I spent four nights in each, and still didn’t have time to see all I wanted to.