You are entitled to your statutory payment tax free and in addition to this ex-gratia payments of up to €10,160 plus €765 for each full year worked is tax free in all cases. That will probably cover your full payment, but if not, you can claim up to an extra €10k tax free provided you haven't claimed this additional tax free sum in the past ten years.
To the extent that your severance payment is tax free, it is ignored for tax purposes and does not impact on your tax credits.
As you are immigrating, you should write to your tax office at the time and advise them that your are leaving Ireland for the foreseeable future, will be non-resident and wish to avail of the "split year basis". In effect, this means that even though you are resident in Ireland, they won't seek to tax on income you earn outside of Ireland after you leave. You also get your full year's tax credits in this case so you should be due a tax refund too (send them a P50 and your P45 too and give them details of a bank account into which they can refund your tax rebate).