DD is nearly 3 and over the last year or so has had a very restricted diet due to various suspected food allergies (under the care of a dietician) and is about to start testing for possible growth disorder (she's very short but not undernourished or underweight)
She's eaten carrots on and off but recently become a little bit crazy about them 
At bedtime she'll often ask for them (tonight she chomped through a bowlfull) and sometimes there's a request first thing when she wakes up. One night she even woke at 3.30am to request one and was distraught when I said no so I had to go and peel one and bring it back for her.
We're kind of amused, and relieved it's not crisps she's obsessed with but I was wondering if it could be at all related to her restricted diet, or allergies (like a craving or deficiency) or if it's likely to be just a toddler obsession thing? Strangely, her nusery were quite surprised when I said how mad she was for carrots as she doesn't ask for them when she's there; it seems to be restricted to home.