Dallat was ordained priest for the Diocese of Down and Connor on 10 March 1951. Following ordination, he was sent to pursue further studies for four years at the Catholic University of Leuven, (1951–55) where he took courses in Sociology and Historical Science. It was a source of some amusement that a man who, as Bishop Patrick Walsh said at his funeral "would never use a paragraph when a sentence would do", obtained further postgraduate qualifications with unusually long titles -"Lic.en Pol et Soc, Lic en Sc Hist."