My experiences only:
My daughter has always had an interest in knives. Right away she was taught "don't touch" and "knives are owies", to the tube that I asked "what is this" the responce was "a knife, knives are owies". I then moved on to teaching her the parts- blade, edge, handle. When she could understand these factors I started showing her proper usage in food preparation. One of my proudest moments was when in a restaurant she asked if she could use a knife to cut her food. She grabbed the butter knife and used it extremely well, doing everything as she was shown. My wife and I shared that look and the next day she was cutting her Pizza Pop with her own knife! Since then she uses a knife on a semi-regular basis, when she asks. For her 6th birthday in May, she received as her own her favorite slipjoint of mine- a mammoth handled John Lloyd trapper she nicknamed the "Zebra knife", as voids in the mammoth were filled with black epoxy giving it a very distinct look.
I was very happy to learn that her 'teacher' In daycare has been teaching her class cutting skills (strawberries and other softer foods). I feel that we are too concerned with safety and making sure that nobody feels pain that we tend to neglect teaching common life skills to our children for fear of getting hurt. When I find myself thinking in this manner I look back at some of the stuff I did, and the other, more reckless kids around me. We got hurt, we bled, and we lived through it without really having our lives in danger! Kids get hurt, but they also heal!
My son is a bit different. Being more active and animalistic, he has just recently began understanding what a knife is and that it is an "owie" at 3. He doesn't handle knives yet (but loves axes)but will when the time is right, and I'm sure that is well before he is 10. I just can't see waiting that long to teach kids how to cook, and to me a major part of cooking is food preparation with a knife. But that is my opinion and everybody raises their kids differently, and by far the greater majority turn out okay because of; or in spite of; our upbringing. I felt like a horrid parent the day I finished sharpening my knife, dropped it and my son picked it up before I could bend down to grab it. A couple of stitches later, the hospital staff laughed and said "see you next time it happens" (after commenting favorably on my quick bandage job), and a year later it's a forgotten memory, he has healed and I'm just left with the guilt- its often worse for us than the kids!
I would differ from most here in that I would not give a folder as a first knife, nor would I have it dull or with a rounded point. Our children will get cut if they are knife users IMO, so why not train them as they will be using further in life? A sharp point teaches them not to get complacent with where the tip is, and an efficient edge shows how to cut/slice without having to force/saw through the item. A small puuko, traditional bird and trout knife or many others are sized appropriately, can be had with sufficient guards if needed, and are fully functional tools. If a FB is not allowed in your area then that changes things- but something like a Cold Steel Mini-Pendleton hunter has fit many young hands well in my experience.
Your daughter has expressed an interest in the specific SAK- nothing wrong with getting her that either- at least we have another lifer knifer in the making- and a lady to boot!! If the knife you get is a folder, I would also suggest dulling it for opening training, but sharpening for when she needs to cut with it.
First "knife" to get things started
Proof in the pudding (okay, pizza pop)
First Khukuri (started chopping lessons this year)
Next generation (will start with something a bit smaller):
I just try to remember King of The Hill. Hank gets a 'boy scout' (different name) to be able to experience some of the camping type Activities that they learned from as kids despite an overly protective parent. He hands his son a nice blue camping knife, then you hear an "Ow", followed by a "did you cut yourself, yep you did, time to get the first aid kit". No freaking out, just a learning experience! Even though it was a cartoon it was one of the most knife responsible shows out there.