Don't know where you can buy one but I have a never fail carrot cake recipe that is dairy free (and nut free). Everyone who has tried it loves it - even the kids. PM me if you would like the recipe.
We didn't have an oven either. Bought a mini-oven which takes a bit longer to cook things but you get used to it... Other than that or baking it at a friends place I have no other suggestions sorry.