Here is one:
http://www.icedgembakes.co.uk/gluten-free-and-dairy-free-baking-recipes/carrot-cake/
This gal is in the UK and also has a book published. Recipes are good. You should be able to find the ingredients no problem.
This gals recipes use no xanthan gum, but I would add 1/2 – 3/4 teaspoon to the full recipe. I found it needed it. But don’t add too much.
Hope it helps.
Teri, Ontario, Canada http://www.TeriLovesCake.ca