The jump pad that accesses the moon levels becomes available when you complete the standard 16 levels. Grannie will give you permission to access the moon when the 16 standard levels have been completed. Completing the secret levels does not count towards unlocking the moon.
When you have collected ALL 2,000 Diamonds and 40 Water Sprites in the game you will be able to press the L button on the 'Title' Screen to switch to Grannie and start the game. Grannie has ALL of the available power-ups in the game to use at once.