Welcome to the forum, Slamsdale.
Generally, cakes with dried fruits (eg raisins, sultanas, cherries, cranberries) and nuts do keep well for long periods, and longer with more alcohol.
However, cakes with fresh fruit / veg, such as apple or carrot or courgettes, usually need to be eaten within a few days, and kept in the fridge if not eaten within a couple of days.
So, if I were making a cake with carrot & apple for Christmas Day, I'd make it not later than 23rd Dec. However, as an alternative strategy, you could make a traditional Christmas cake, but eat only small slices over a long period of time.