Welcome to the forum!
I would not advise taking on this much travelling in 1 day to be honest - even in June, when it is still bright here after 10pm at night..
Dublin to Doolin (and the Cliffs, as they are beside each other) will take at least 3.5 hours. June is a very busy month for tourists, so you would need to allow longer to get around and between destinations, as there will be more traffic on the roads. You will need at least 1-2 hours for Doolin and the Cliffs of Moher - I would suggest taking a Cliffs of Moher cruise
(of course ;) ) This takes 1 hour to complete and leaves from Doolin several times a day, starting at 10am in the morning, so if you really wanted to, you could drive to Dingle afterwards.
The drive from Doolin to Dingle will take approx 4 - 4.5 hours, so I would advise you to stay overnight in Doolin or the North Clare region, and then travel onwards the following day.
I hope this helps with your travel plans!
All the best from Joan at Garrihys Doolin2Aran Ferries