There is no extreme, direct physical danger, per se, but you can pick up any number of viruses from your patients. Many of them have not yet mastered the art of covering their mouths when they cough.
Also, because kids can be rambunctious or out of control at times, you also might wind up with your stethoscope wrung around your neck or a tongue depressor jabbed into your eye. We don't want to misrepresent kids though—on the whole, they're truly wonderful, darling little angels. But let's just say that some of them are fortunate that smacking knuckles with rulers is now out of vogue.