I would also mention that most people's children are safe from anxious off-lead dogs, because anxious dogs give people a wide berth. In my experience most dogs, other than daft bouncy puppies, do. (Not that I condone letting a puppy jump up at a child or anyone else)
If your child doesn't get the dog pinned in somewhere that they can't escape (unlikely even with the most persistent child - if the dog can get away, it will), then they are quite safe from "snappy" dogs.
There are actively dangerous dogs about, but they are happily few and far between.
Most children who are bitten by dogs are bitten by family dogs that they have been allowed to tease/torment and haave then been left alone with.
No child should ever be allowed to treat a living creature as a toy - it usually isn't the child's fault, as many are too young to realise that they are hurting or frightening the animal; and no child, no matter how gentle, should be left alone with any dog, not matter how sweet-natured.
It's common sense - but as they say, common sense is rarely common.