The priest in question violated canon law, and possibly the moral law, in refusing to baptize the baby. He needs to be informed of what the Church teaches. In cases of urgent necessity and specifically with cases of children under the age of seven, canon law requires that they be baptized without delay (CIC 867 §2). When there is danger of the baby dying, there is no requirement that the parents be present, that they be practicing Catholics, or even married in the Church. Thank God for that doctor and other doctors like yourself.