Flying into Shannon if possible makes a lot of sense and cuts down on time spent travelling from Dublin to the west of Ireland.
You are moving around a lot which can start to get hard work unpacking and packing up again each morning. Don't underestimate how long it will take to drive between places in Ireland. Distances may not seem far, but will take a lot longer to cover than you might expect. Roads are narrow and slow often with a lot of slow moving traffic. If using google maps it is recommended to add 25% to their driving times AND THEN ADD ON TIME FOR STOPS.
What is the attraction of Galway? By the time you get there from Dublin, you aren't going to have much time to enjoy the place or explore much of the surrounding area.
Day 2 is a lot of driving - probably six hours PLUS time for the Cliffs of Moher
What is the purpose of Day 4 - what are you intending to do/see on the way? You could actually do Killarney, Ring of Kerry and Kenmare from Dingle and then head back to Dingle for the night, making three nights in Dingle.
Dingle to Cork is just over three hours drive, so not much further than from Killarney or Kenmare.
What are your plans for Cork? If time allows, don't miss Cobh, an attractive town of brightly coloured housesand the Titanic's lasrt port of call.