It's likely she's not ready, but clearly getting there. Here's a wonderful, informative website you might find helpful. It gives a few variations on "readiness" checklists, plus tips on various training strategies, the best ages to start them, and the advantages and disadvantages of each approach: http://www.parentingscience.com/toilet-training-readiness...
It sounds like you are happy to let your little girl take the lead. That usually works very well – almost all the kids I've known who trained in a week or less simply decided they were ready. They made the developmental leap because they wanted to. For most of them, this happened somewhere between 23 and 40 months (with boys usually a bit later). It's also helpful to know that nighttime training and pooping are often separate steps. Rarely, they happen before daytime pee training, but very frequently, they come later (especially night dryness).
One of the biggest features in readiness, in my observation, is the child's ability to notice sensations and realize ahead of time that they are getting signals to pee or poop. This takes awhile, and it has sometimes seemed to me that parents who make too big a celebration out of the occasional success are probably distracting the child from her sensations. Happiness and congratulations are positive reinforcers, and should not be stopped, but a quieter child might need a quieter smile and comment.
The other thing to consider, as you celebrate, is that the achievement is the child's, and you don't want to encourage her to think she's doing this for your happiness. She wants success, just as with walking and talking, when she's ready. Let her know you're proud of her, but be sure she knows it's even better if she's proud of herself.
From your description, your daughter is doing a great job of sorting out when she wants or needs to try the potty. She can only do this at her own speed. Quiet encouragement will help her get there.