For the "Fanning" name you need a male with the name "Fanning" - in other words the y-dna only passes from father to son.
Have a look at
the Fanning DNA project , and look at the various tabs along the top like "Patriarchs" Contact the organiser to discuss it, I am sure she would be please to help. They have research on Fannings (but most of them are Americans who have no idea where they came from except "Ireland")
From memory there was some debate as to whether they always were in Sligo or came from Limerick - my own view was Limerick, but that was not based on extensive research!
DNA is a complex subject, and there is a lot of misunderstanding/misinformation/prejudice about results and how they should be interpreted, so take care. Having said that it can be a great help in establishing where your family came from. If your DNA matches theirs, then you have made a big step forward.
I had advised them last year to try to find people in Ireland to do the test, so they should be very pleased to see you are interested