James, does your daughter spend time with her friends, talk on the phone, or email pals? Just as she enjoys and needs the company of people her own age, so do you. When I started dating, I joked with my daughter that

if she were willing to spend her Friday night at home with me, I wouldn't go on the date!
if she were willing to spend her Friday night at home with me, I wouldn't go on the date!! She got the point.
It may also be that since you're recently divorced, she's just getting used to the idea. She may be afraid of losing you, or jealous that someone else may take her position in your life. Assure her that nothing will ever replace the relationship you have with her. Give her lots of reassurance and, if possible, go on your dates when she isn't staying with you or when she's spending the night at a friend's.