The Roma and Irish Traveller are different groups of people. The word "Gypsy" is really confusing the issue. The Irish Traveller have had a few genetic studies done on them and they are just a subset of the Irish. They have drifted a bit due to endogamy.
This is a bit difficult to see but it is from the Irish DNA Atlas which hasn't been released yet.
They are thought to have diverged from the general Irish population about the 1300s.