Yikes.
This could have been much worse, I'm glad to see that it wasn't.
Puppies tend to bite - they are puppies and don't know any better yet.
This event makes me think that this person didn't know or understand that a dog of any age should never be left alone with a child - Including "In the same room but not in sight". - I hope that they realise this now.
In the short term, again ? puppies bite.
In the short AND long term - No matter how well trained or well behaved the dog has been in the past, people, including children, can inadvertently make the dog feel threatened one way or another. (There are always clues, subtle or otherwise.)
With no adult to step in and stop the child doing whatever it is doing... a dog is an animal, and when all else fails in dealing with a situation, it will revert to instinct.
Especially a risk if (and this is a slightly crude explanation) the dog perceives the "pack hierarchy" in such a way that considers itself to be above the child.
In this instance, it is possible it is just the puppy being a puppy - hard to say given the naturally limited information (very hard to get a feel for a dog?s behaviour from a few lines of text!)
I am a little uneasy with the idea of getting rid of the puppy, but it does sound like this person does not entirely know how to handle this dog (again, with the limited information from original post, ect ect.. I've not had the chance to read the entire thread...)
Whenever obtaining a dog, it is always a good idea to have first researched usual characteristics of the breed(s) being considered before obtaining a puppy, because if they do not have the time to correctly train and stimulate the dog, it will NOT behave and WILL be a risk to have around.
If they are sure they can handle this animal, train it, and raise their child to respect and command it as well (if not better) as they can, keep it!
But the most important thing to remember is that this dog is an animal, and must be treated like one - with kindness and love, but NOT as a son or daughter, as I have seen so many people make the mistake of in the past.