Useless suggestion given its the middle of winter, but a good hot burst of bright sunlight kills all sorts of nasties, including mould. Its the UV light. Its no coincidence that mould grows in DARK places.

Most essential oils are so potent they'll kill anything (check the bottles - a lot are actually marked as poisonous and will kill people too) so I'm not sure I'd use them on a cot where a baby might be gnawing on the bars. Oil of cloves you can stick in your mouth for toothache and tea tree oil is in a lot of soaps and skin creams so if you're going to use any essential oil I'd be using one of those two.