Preheat oven to 180 degrees celsius (fan-forced). Grease and line a deep loaf pan with baking paper and set aside.
Sift the self-raising flour, bi-carb soda, salt and cinnamon into a bowl. Add the caster sugar and mix together well. Make a well in the middle of the ingredients.
Add the lightly beaten eggs and the melted coconut oil and mix together.
Add the grated carrot, drained zucchini (see note) and apple and fold through.
Spoon the mixture into the prepared tin, smooth down the top with a spoon and bake in the oven for 50-60 minutes or until cooked through when tested with a skewer. Leave to cool in the tin for 10 minutes before carefully transferring to a wire rack to cool completely.
Store in an airtight container at room temperature for 4 days or freeze for up to 1 month.
Strain the excess liquid from the grated zucchini by placing into a strainer and squeezing with a tea towel or paper towel.
If your bread is browning to quickly in the oven, lightly place a sheet of foil over the top and continue cooking.