There is a probability that Dr. Princess might be the girl Ice King was going to marry (Betty). It is shown in this picture that they share many features like the lab coat and the same style of glasses, except that the skin color is different. It might be that the skin color has changed over the years. It is nor confirmed that they are the same yet but there is a probability. It was stated by the Ice King that his favorite part of Doctor Princess was her heart along with other components giving credibility to this particular theory.