You can freeze an un-iced carrot cake for up to 3 months, well-wrapped in clingfilm. Carrot cake is very forgiving. As an oil-based cake it's very easy to throw together without much advance warning.
Grease and line the base of a 20cm/8in springform cake tin with baking parchment ... oil and milk together and stir in the grated carrot. Add the egg mixture to the dry ingredients, stirring ...