German Australians do cookies (except if we're only 1/8 German and maybe don't have Christmas) , but my childhood was full of people making puddings and cake and Christmas pudding icecream. Cherries are also very much Christmas food in Canberra.
I have my Christmas on Christmas Eve because that's when I'm invited to the big dinner with the presents. When I was a kid I used to be invited to my aunt's on Christmas Day, but the evening meal makes a lot more sense in summer. We also have Boxing Day and (in Canberra) the day after Boxing Day. That's when sales start, and the Sydney/Hobart Cup and the cricket.
me? I get (as I said) Christmas Eve with friends, and every evening I light candles for Chanukah, but the rest of the time is pretty much work. Except taht this year I seem to have a wild social life planned (but no plum pudding icecream! and also none of my aunt's recipe for mini Christmas cakes that take five minutes to pull together).
We bake for Santa, december the fifth. Pepernoten, small irregular cubes of "Lebkuchen". Kruidnoten, small crunchy balls with spices and figurines of this same dough, called speculaas. Speculaas is sometimes filled with marzipan. For New Years eve we bake oliebollen, (round Berliner with currants and raisins). A local tradition for New Year around here is the baking of Speckendicken", just like they do in Ostfriesland. And to tease the company it was a game to put a bit of an old sheet in some of the Speckendicken to see someone chew and chew and chew.