While preparing to enter Maynooth College, Quarter was visited by a priest who had served as a missionary in the United States. The young man was moved by the priest's stories of the dreadful plight of Catholics in America (many of whom were without priests, churches, or the sacraments), and resolved to dedicate himself to the missions there. Having obtained permission from Bishop James Warren Doyle, Quarter departed from Ireland in April 1822 and later landed at Quebec, Canada. Following his arrival, he was rejected at the seminaries of both the Archdiocese of Quebec and the Diocese of Montreal on account of his young age but, journeying southward, was finally accepted at Mount St. Mary's College in Emmitsburg, Maryland. While at Mount St. Mary's, he became professor of Greek and Latin, as well as sacristan, in 1823. He completed his theological studies in 1829 and then went to New York, where he was ordained a priest by Bishop John Dubois on September 19 of that year.