She is the former girlfriend of Carl Gallagher.
In the seventh season, she does not want to perform oral sex on Carl, due to his being uncircumcised. He gets a late circumcision for her and she finally gives in. After learning she has gonorrhea, Dominque's dad goes after Carl. Carl later sees Dominique kissing another man, he takes a picture and shows it to her dad. The remain broken up when Carl is now in military school.