Oh I'm sorry, I don't think anyone should be alone on the holidays. Where is your family, just not close by?
When I was little on the holidays I remember doing different activities with my family. Thanksgiving Day we would have dinner, but my fondest memories are of putting up the Christmas tree that same day/weekend and decorating it with my brother and sister, and making pumpkin pie with my Aunt Rosie. My mom used to give us a stack of construction paper and we would cut out paper snowflakes and decorate them with crayons, markers, glitter, stickers, etc. A fun activity that you two can do together; you cut and she can decorate. Hang them on the tree, from the ceiling, you can have her help you string up popcorn too. That kind of stuff keeps you busy too and passes time pretty quickly.
For Christmas we used to spend hours, days even, baking cookies and pie. All kinds of them, and of course when you're a kid eating them is just about the greatest thing ever. I know your daughter is still fairly small, but those are the kinds of things that I reflect on in my childhood that was a tradition for a long time and they are great memories.
I have spent the holidays alone before too, and I know its depressing, but try to make it good for your daughter and maybe start some traditions for yourselves. Perhaps just being you two will make it that much more special to her later in life. Happy Holidays!