A lot depends on what your Killarney plans are. Hopefully you aren't staying in Killarney....Rick Steve's has it listed as one of Europe's top ten tourist traps....and he's right. Great things to see near Killarney but the city itself is not great. Wonderful places nearby.....Kilorglin, Kenmare or Castlemaine offer much better places to stay and experience real Ireland right near the great sights without the leprechaun-y gift shops and Holiday Inns..
If in Killarney you are just seeing the things in the Killarney area you would be right near the wonderful south side of the Ring of Kerry and the Skellig Ring which you could spend many days fully exploring.......ring forts, Abbey ruins, castles, ogham stones, insane scenery, the Glen, Skellig Michael, horseback riding or biking and the Cliffs of Kerry.......far better than the tourist overrun Cliffs of Moher....it's a long drive to Doolin....with such short time why bother....when better cliffs are right there. There are many wonderful,welcoming small towns like Kenmare, Sneem, Waterville, Ballinskelligs, Portmagee or Cahersiveen.....with pubs, shops and restaurants.
Also fairly close is the Dingle peninsula with Slea Head drive, the Blaskets and lots to see to fill a couple days.
The Beara Peninsula is close by Kenmare and is wonderful, beautiful Ireland without the crowds. That can easily fill two days.
The southwest we have spent months in and not exhausted it's magic or treasures. It's got more than enough to fill 2-4 days. Racing around is extremely counterproductive to really experiencing Ireland so I'd urge you see the stuff near Killarney without staying there and if you must move on for two more days do something reasonably close and very rewarding like really exploring the ROK, enjoying the wonders of the Dingle peninsula or the quiet haunting beauty of Beara. But staying 3-4 days in one spot as a base - there is PLENTY to do right nearby........and the joy and magic comes with the interactions with the great Irish people and the discoveries you make yourselves.