Just my two cents, but I think it is okay for the child to play with the puppy, supervised.
Absolutely do not let the child do anything that will actually hurt the puppy. I think everyone agrees with that. If the child will not respond to simple commands at all, then that would not be a child I would trust to not hurt the dog. As far as doing things that annoy the puppy, such has handling the puppy's face, I would be a little more tolerant, as discussed below.
Puppies generally have pretty good tolerance for play. As part of the socialization process, it can be very beneficial to handle all parts of a dog when they are young so that they will not be too upset by it when they get older, and have to endure uncomfortable or unusualy treatment by the vet or the groomer. For this reason, I purposely handled my dog's feet (which initially he didn't like at all) and put my hands in his mouth to check his teeth and run my fingers along the gum line. I held his muzzle shut for short periods of time (not forcefully, of course). I have also read places suggesting you should also handle the dog's genitals, but I couldn't bring myself to do that. All of these things are things that he was likely to encounter by the vet and a groomer when he got older.
I would first do all of these things frequently yourself to help socialize the dog and get it used to such handling. I would also closely supervise the child's play. I would say you should instruct the child not to do these things. Hopefully, the child will respond, at least for the most part. If the child does not obey one hundred percent of the time, but is pretty good, I would not get too concerned, assuming your puppy seems to be tolerating the contact okay. You should be able to tell if your puppy is enjoying itself.
All this being said, at eight weeks, your pup may be a bit too young for handling by the child other than letting her pet the pup gently while you hold it. When it gets to be closer to 12 weeks, a little more interaction might be in order.