Mine eat the baby carrots too. After Beamer has been groomed he dashes to the fridge and as soon as I open it he scratches at the vegetable drawer like he is anxious to get it open - he wants his carrot
I only need to mention carrot and he will go to the fridge!
I did ask the vet if it was OK for the Yorkies to have the raw baby carrots and she said it was fine.