Traveling from Galway to Killarney in September

We do not have a car. Is there a way to travel directly from Galway to Killarney with no train or bus changes?

I do see bus service Bus Eireann that goes between Galway to Limerick then Limerick to Killarney with bus change in Limerick. It seems the fastest - yet there is only 15 min between arrival of the bus in Limerick and the departure to Killarney. Will that be enough time??? We will have luggage ( Carry on and small backpack each.)