I don't think there's an objective age on firearm safety. I mean, we can all agree that.. say, toddlerhood, might be a little too young. But generally speaking, it's completely subjective as to the age when you're speaking about motor skills, responsibility, discipline, respect, understanding. Especially at the age of nine, being such an age between childhood and being a teenager. One nine year old might think guns are no different than toy guns and flippantly wave it around, while another nine year old knows the ropes better than an adult. I'm not saying this young girl was irresponsible, don't get me wrong. Just as an answer to the question, I think it's completely subjective.
That said..... I think where objectivity does come into play is what weapon you choose to train a child with. When I was learning to shoot, I was given the best fitting, easiest firing, calmest handgun for my physical size, being a novice, and taking into account the environment. I would be really curious to know why they felt an Uzi, of all guns, especially on auto after ONE single shot, was a good idea. Anybody experienced in any sort of gun handling, even if your only knowledge is videogames (the one time that might come in handy), knows what an Uzi is like. I wouldn't even want to look at one the wrong way.
We can all agree it's an awful, awful tragedy. The girl will grow up always knowing what happened, even though it wasn't her fault; and the instructor and his family lost a life unnecessarily. I don't mean to point fingers or anything at all, I just hope some thought goes behind the difference between age appropriateness and weapon appropriateness. Unfortunately, it'll cast a negative light on firearms when it should cast a negative light on the amount of education and responsibility required.