I think a good family dog has more tolerance for things kids do. I've had lots of dogs, GSDs, Labs, mixes etc with my kids when they were toddlers and although watched, there were occasional times where the kids would do something which I corrected them for, but the dogs were all very tolerant and would walk away if they were being bugged. One time my 2 yr. old son squeezed my GSD's muzzle and turned it like a door knob. He didn't know what he was doing. I told him "no." But it had already happened. The dog made a little wincing sound but put up with it.... and then walked away, quite unperturbed. Another time, my son fell off a table onto the soundly sleeping GSD and knocked the wind out of the dog. He grunted, got up, walked across the room and lay down again.....unfettered. Small kids do weird things and a dog with a decent temperament, as well as proper handling, should be able to tolerate a little bit, especially if it is not trapped and free to leave the immediate area. That is my opinion after having lots of dogs with young children. Dogs have hung out with kids for eons, gone fishing with them, gone exploring and parents didn't supervise them constantly...that's a little older kids anyway.
Back then, when my kids were small, not so much was said about supervising kids and dogs. They just kind of went together. My GSD would hang out with my kids without my watching every second. He was their pal and he loved them like crazy....watched over them, put up with stuff, just wagged his tail and was thrilled to be with them...never one iota of resentment or "crossness" of anything to do with those kids and their friends.
This is indeed a tragic thing. I do hope the child recovers OK. I would definitely destroy the dog. It is unfortunate but simply not safe.