A.,
I feel so sorry to hear your sad tale. It is so hard to pull yourself out of depression and move on with your life. From what you say, the father of your baby is committed to another - and will not leave her. If that is true, then you need to find a way to let go and move on. For your sake, and the sake of your child... I would suggest joining a Mom's club, or some group where Mom's can meet and talk and children can play together. Check your area to see if there is anything available to you.
I know you don't want to hear about "Finding God" but let me just suggest to you that often there are organizations within your local churches that might offer friendship and support to you during this time. Check out what might be available if you started going to church. Trust me, being around other people, especially other people who are caring and supportive is going to help you.
You say when you go out that your daughter is safe and well cared for... do you have the support of your own parents or family? I hope so. Having family love and support is going to be really helpful, both to you and to your daughter.
It is good to be focused on your child and her needs, but don't let her be the only thing you care about. You need to have something for yourself too. I hope you will talk to people.. friends, co-workers, family.. and look for support and help from people who care about you.
If you start feeling hopeless or suicidal, PLEASE talk to your doctor about anti-depressants.
Read some good books that help with Self Esteem.
Most of all... look for support groups, and support from friends and family who care about you and your daughter. Reach out to people around you -- once you start to be involved with others - and get focused on other people, you might be able to move on from this guy.
I wish you the very best.
M.