Personally I don't think a child that young should be shooting an Uzi.
That said I'm all for gun ownership and I own quite a few between handguns, shotguns, AR, rifles, etc. I enjoy going out to the shooting range and I LOVE skeet shooting. My husband also hunts and eventually I want to go hunting with him. My husband also has his conceal carry permit. We are both very serious about gun safety though and I don't see any problem with us owning guns. I do not open carry at all and have no desire to really do so. Still undecided if I plan to get my conceal permit or not. I would like to get a lot more experience with my hand guns before I make that decision. That's just my 2 cents though.
I do think it's very unfortunate what happened and I feel bad for the little girl though.