Your concern for your daughter shows that you have a core of strength that you may not even have known is there. You would be only human if at times you wished you didn’t have to get up in the morning. But you do it. And your love for your daughter is at times bigger than the depression. This is something precious to hold on to.
You may not be damaging your little girl but you are certainly affecting her. She is drawing a distress that she may not have the words to talk about. Most children worry that their mother’s depression is somehow their fault. Some worry their mother will leave them, instinctively sensing that their mom sometimes wonders if the family would be better off without her. Sometimes kids become overly responsible and “good” in their efforts to make a parent feel better. All of these are normal kid responses to an abnormal situation.
If you haven’t already, please do tell her that you are sick, that it is not her fault, and that you are the one who has to fix it, not her. Tell her about your appointments and that you are taking medicine so that the two of you can have fun together again. I did find a couple of books written for children whose mother is depressed on Amazon and Barnes and Noble. Pick one that is consistent with your beliefs and values and use it as a way to invite your daughter to talk.
Since you are a single parent, she probably doesn’t have another adult in the house to turn to when you are particularly down. I hope you have family or friends who can piitch in at times like that. It would be helpful if you could arrange for her to spend time with people who enjoy her for a few hours a day, so that you both get a break. She needs a break from your pain. You need a break from feeling responsible for her so that you can focus on working on whatever activities are helping you heal.
You didn’t mention whether you are in therapy. I certainly hope so. Generally the treatment of choice for major depression is a combination of medication and talk therapy. Furthermore, a therapist might be able to include your daughter in some of your sessions or help you figure out how best to make sure you both get the support you need at home.
I wish you well.