Thanks for the additional info!
From what I can see, it is possible to use public transport
from Moville to Dublin Airport, that would be a 5 hours journey (Bus 933 from Moville).
If you'd rather go with a chauffeur company or shuttle service to save time, there is Sean Crumlish
in Moville or Donegal Executive Travel
, also operating on the Inishowen Peninsula. I would suggest asking your hotel for more shuttle or chauffeurs companies in the area.
Another option that also comes in mind would be to have a chauffeur or taxi drive you to Letterkenny or Derry-Londonderry instead of going all to way to Dublin Airport. From these two transportation hubs, you can take direct busses to Dublin Airport (which would be more affordable than a chauffeur).
Let us know what you end up choosing or if you need anything else for your trip in Donegal.