Is The Queen The Head Of The Church Of Ireland?

Ireland is actually a divided country, and I believe the Anglican church was disestablished there in the nineteenth century.

The main part, the south, called Eire, is largely Catholic.  I have no idea if the Anglican church is there at all.  The northern part, Ulster is still part of the United Kingdom.  Here again, I am not sure how well represented the Anglican church is there either.

The point to grasp is that the monarch is the titular head of the Anglican church and the Archbishop of Canterbury is the spiritual head of the Anglican church wherever it is found in the world.  That includes India and Africa.  The monarch is not the titular head of any other church, Catholic or Protestant, even when said churches are located in Great Britain.