You are doing an amazing job and I think you are being too hard on yourself.
I would talk to her and just have a conversation about the situation and how it is not for ever.
Is it possible for you to have a set up together for part of the day, so even though you are working you are interacting with her as you would a colleague. She can have her own projects to do.
She is seeing you work, she is seeing your work ethic and you are both together and she is safe with you. She would never get to see this and how hard you work for both of you.
Can you set a schedule for the day or show her your schedule, you can both do a to-do list. As someone suggested up stream, give her a couple of chores to do to give her some responsibilities. Can she be in charge of drinks and snacks at 11? Can she put a washing load on or unload the dish washer.
Can you do chair yoga together at a certain time.
She is going to be fine. Scoop her up and give her a hug.
Best of luck
You are in this together, try to become a team. I know she is only 9 but a little bit of responsibility would not hurt her and actually help her grow.
Can you also block out your calendar for 1/2 hour a day just for her. Go for a walk or something.
You do need to talk to your boss about work life balance.