You sound like a responsible Dad, and she sounds like a responsible girl.
I got my first knife at 6. Scout-type slipjoint. My dad didn't think it was the best idea, but he let me buy it with my own money (50 cents!) and I carried it everyday until high school. I only cut myself really good with it once - trying to split a black walnut. I probably needed a stitch or two, but didn't get one. I still have the scar, but my finger works just fine, thank you.
My daughters are 6 and 7, and have been cutting, in the kitchen, under my spervision, since 4 1/2 years old. If they showed an interest in owning a knife, I would happily pick one out with them - but for know, they think they're kinda scary, and are happy to have me take care of most of their cutting needs. They've each used the scissors on my Squirt and Classic, and the older one has done a couple tasks with my (razor sharp) Para2. Not that they're ready for THAT on their own.
At this age, I'd start with a Classic or a Peanut (if she has the strength and coordintation to open it,) let her hang onto it, but only use it with supervision.
I wouldn't dull it - that would only make her push harder. I also wouldn't worry about rounding the tip, though I may avoid a particularly pointy tip (clip point or such.)
Make it CLEAR which side cuts - If it's a thin blade, kids can't always tell. At one point I found my eldest about to press down on the edge of a mini-santoku to press the spine through some cucumber. Disaster averted, but a close call.
No matter what you do, expect her to get cut at some point. My daughters are very active, and they fall from bikes, skateboards, scooters, roller blades, balance beams, and even running. I keep a healthy stack of bandages nearby, and don't panic when performing minor to moderate first aid. Neither has cut herself yet, but they see pain as a (painful) part of growing up.
As an aside, the other day, my 6yo fell off her scooter twice. She was very concerned that she has bruises all up and down her legs. Then she got back on and rode away.
Her upcoming birthday would be a great time to induct her into knife owership.