Sorry to hear you are having a tough time. Quitting your job is a big decision with lots of implications. I would not decide one way or the other while you are unwell (depressed) as it is easy to lose perspective. It would be worth taking into account that not working can also impact on your mental health. For example many guys self worth and identity is tied to their professional skills so when this is taken away mental health can deteriorate. Loss of income and associated financial stress could also have a negative impact on your depression and relationship with your family.
I'm not saying leaving your job is the wrong thing for you (your decision) but it might be wise to concentrate getting on top of your depression in the short term. Good on you for going to the GP and a psychologist. There are also many things you can do for yourself like concentrating on getting regular exercise, enough sleep and having a good diet. No doubt you have heard all that before.
A more left field thing you could consider would be putting time and effort into your relationship with your daughter. This could include taking and helping with her homework. Trying to do regular outdoor exercise with her will be a positive for both of you. Just do whatever she is interested in whether it is walking, bike riding, swimming or basketball. Many men who struggle with depression lose motivation and can't find joy in anything. For me seeing my children getting out there having fun is the best way to get me out of the house and lift my mood.
Is there any chance you could reconnect with some of your old school or workmates? Having a few trusted male friends who can support you would help immensely. Even better if they have children a similar age to your daughter. I think it is great for introverted kids to have a group of friends outside of their school environment. You will understand what I mean if you can get this happening.