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.

Cakes are best stored in airtight tins rather than plastic boxes. Once a cake has been cut, the cut surfaces will start to dry. Covering them with a piece of aluminium foil minimises the effect.