I was always my mom's kitchen helper, and this is the kind of stool she had us use: http://www.ebay.com/itm/Cosco-Retro-Chair-with-Step-Stool...
Even at a young age none of us toppled off of it. It was quite stable and I have wanted to get one for my own kids.
Having the fold-out steps is nice since the kid can stand on any of the steps, depending upon how high up they need to go.
Otherwise, I sometimes just bring my ingredients I need to prep to the kitchen island and sit with the kids and give them a butter knife or something really safe so they can "cut" some of the food. My little sous chefs are so helpful ;-) When my (now 3 year old) was a toddler, he always wanted to watch me cooking on the stove, so I put him in my Ergo on my back and let him watch me. So much easier to have him in there than reaching into my pan.
ETA: J. S. makes a good point about her probably wanting to climb out of that stool at will, so I'd do something that allows her to come right up to the counter, yet lets her back down when she wants to. Like this: http://www.amazon.com/GuideCraft-High-Rise-Step-Up-Natura...