I think that’s exactly right, Cunctator.
The mythical origin of the name is that there were three queens of the Tuatha Dé Danann, Ériu, Banba and Fódla. The name of the country was to alternate on a three-year cycle, but ended up sticking with Éire.
If you were looking for an Indo-European root, I think “peace” may be a bit optimistic. It could be cognate with the word “Arya” (as in “Aryan”), which is related to the word “art”.