You know booze won;t make any of the things you mentioned better. But it really will make them worse. It would just add another stress factor to the list.
Instead, take the list you wrote and think of one small thing you can do to improve things, just a tiny bit.
The thought of another shitty Christmas - think of a three things you can do with yoru daughter that you can enjoy this Christmas - watching a shared film, going to a carol service, looking at the lights and window displays, a few food treats, dancing in the kitchen to Christmas songs, making some decorations together, cooking together etc - just do a few of these.
the thought of how much work I have to do, despite being finished for the year, the thought of having to go back in January. Put these out of your mind for now - allow yourself a few days where you don;t do any work or think of work at all.
The thought of being a shitty single mum to my daughter who deserves better than me - what woudl a better mum do? Do it.
In terms of that urge of wanting a drink, plan some good treat alcohol free drinks - Virgin Mary, Virgin Mojito, alco-free beer or shandy, cranberry an draspberry with sparkling water and ice, Apple and ginger with mint etc. Get them all in for yourself so you and your daughter can have some festive drinks together, or a celebratory drink to mark the end of a tough working day. A long, iced mocktail does the trick.