Plenty of gluten free mixes out there for a once a year gluttony. I don't stress anything but gluten for very rare occasions. As long as your day to day is on par... Enjoy your birthday. It's anti-stress. Don't complicate it, have what YOU like.
Just have it preferably gluten free and vegetable oil-free
You might find something suitable in the Sweets section of my Recipe Index.
I would recommend the Chocolate Sponge Cake, filled with fruit and coconut cream (there's advice how to whip it here on paleo hacks)
However, what I consider birthdayish is to be served my favourite meal, especially if it's at a fancy restaurant. My meal of choice is grass-fed steak served with buttery zucchini and wilted greens, at Rockpool in Melbourne :D
CHocolate covered strawberries. Also, my grandma used to do this thing where she would freeze bananas and then stick them in melted chocolate and the chocolate would instantly freeze coat on to the banana. Very tasty. Stick a popsicle stick into the banana before freezing for easier handling.
There are also a number of cake recipies using permutations of coconut flour, artificial sweetner, banana, almond flour, etc. Not perfectly paleo but better than a slab of sugar.
Heavy cream mixed with a bit of vanilla extract and some cacao is quite good when whipped into chocolate whipped cream. You can get by without any artificial sweetner, but a dash of stevia is nice also.