This topic is close to my heart because I am an only child and struggled with feeling lonely. Unlike your daughter, I was very shy and so would never have just run over to another child's house to hang out. It is great that your daughter is extroverted, and I understand that you are anxious that her spirit and social nature will be crushed if other children continue to reject her.
Divorce may be particularly difficult for only children. This is true for children without any siblings as well as virtual only children, those who are separated by seven or more years from their closest sibling. Children with special-needs siblings can also feel like only children, particularly if the sibling is unable to engage interpersonally.