You can get a PPS from any local Social Welfare office in the Republic. The Dundalk office can be found at Government Buildings, St Alphonsus Road, Dundalk, phone number 00353429392600.  You will need to bring proof of ID (e.g. passport or driving licence) and address (utility bill should suffice).   If you are an employee in the Republic you will usually pay Irish income tax through the PAYE system in the Republic.  If you remain resident in N. Ireland you have to declare your earnings from the Republic to HM Revenue & Customs. You may or may not have a balance of tax to pay in the North having been given a credit or relief in respect of the Irish tax you have paid in line with the double taxation agreement between the UK and the Republic. You can contact FAS in Dundalk (phone 00353429393400) for details of jobs in the area or indeed Newry Jobs & Benefits office may have details of Dundalk vacancies. 

Your qualification will generally be recognised in all other EU states but I would suggest that you contact the Irish National Teacher's Organisation (phone 0035318047700) which is an all-island body to check your position. The recognition of academic qualifications is dealt with by National Academic Recognition Information Centres (NARIC) in each European state (contact details of UK one below). More information on recognition of professional qualifications is available on the European Commission website at

http://ec.europa.eu/youreurope/nav/en/citizens/education-study/qualification-recognition/index.html