Not being able to carry out the whole activity is ok. It is the effort that counts. It's the act of getting up, getting ready and getting out the door that makes the difference. If you cannot finish what you started, that is ok. Pay attention to the messages you are giving yourself about how you feel. Telling yourself that you are a failure when you complete at least half of a task, when just before that you were not doing anything at all, is setting yourself up for feelings worse. You have to try rewarding yourself for making an effort. That way, you will want to try again.
If you are focusing on seeing your therapist, it is going to seem like forever until you see her. It is hard, but try to distract yourself. Even if you spend the day trying to do something, it will go faster than if you just sit and think. For example, go out with your daughter and treat her to something special. See a movie, even if you don't feel you can concentrate on it. Let your daughter be the one to enjoy it and find joy with her response. As long as you are doing something, the time will go faster.
Going to church is a wonderful thing to do for yourself. It is a healthy environment that provides support to you and may even bring you some peace. It also lets you be around other people without having to have the energy to interact that much. Faith in God is always important when you are feeling down. It gives you hope when you may feel there isn't any.
It is very normal to have trouble eating and with sleeping too much when you are depressed. These are symptoms of your thought process. Keep trying to eat as much as possible. It is ok to go off your normal diet when you feel like this and eat anything that appeals to you, even if it's ice cream for dinner. You have to keep your energy up so you will feel strong enough to cope with how you feel.
Make sure you plan something to do tomorrow when your daughter is at school. Break your day up with small activities or plan a middle of the day outing. It will make the time go faster.