Correct me if wrong but don't schools in Ireland start back earlier, so 1st Sept would be within school term. Hence less people travelling anyway from or two holidays.
They return the last week in August, all having closed early-June. But you'd be surprised how many people actually go on holidays in May and September in Ireland, a local school where I live in Cork complained of an absence rate of nearly 25% in the first two weeks of September, calling for greater regulation of children missing two weeks of the school calendar year (which by law supposedly is a max here), and its something replicated throughout Ireland really, much unlike in the UK where they are very strict with people taking their kids on holiday during school terms I understand?
The peak months of holiday travel in Ireland would really be July and August with the second half of June also very busy.