Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a large bowl, mix the gluten-free flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs and sugars until well combined. Add the oil and mix well.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the grated carrots.
Pour the batter into the prepared baking pan and bake for 30 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
For the cream cheese filling, beat the cream cheese, powdered sugar, and vanilla extract until smooth. Fold in the whipped cream.
To assemble the trifle, cut the cooled carrot cake into cubes. In a trifle dish, layer the cake cubes and cream cheese filling, starting and ending with the cake. Chill in the fridge for at least 2 hours before serving.