She sounds like she's doing a great job of working things out in her own way. I wouldn't discourage the questions - she needs to feel she can talk to you about these things. I wouldn't even worry about her saying inappropriate things to playmates, because it'll probably just go right over their heads - unless they have lost a relative (or pet), they just won't understand what she's talking about.
I can't imagine any other parent would get upset if they realized that she's trying to make sense out of death for the first time.
My boy was about that age when he got obsessed with death after seeing some of the animals at the Fernbank museum. "Is they real?" "Yes, but it's not alive anymore." It was the discovery of the difference between "real", "real and alive", and "real but not alive anymore, and of course, "not real" (like the dinosaur exhibit.)
The "Is it real?" and "Is it alive?" questions went on for months. Occasionally, he would say something that would completely jar grown-ups (like, if her were mad, he would say he wished we weren't alive, or that HE wasn't alive. He just didn't realize the weight of his words. He didn't realize that it can CRUSH anyone when you say something like "I wish you weren't even alive!" He just didn't understand how that was any different from "I need a little time alone now." ) We gradually worked through that, too.
Just the other day, they were talking about the election on the radio, and I said "Remember when we were talking about how this year we choose a leader for our country? Well, that story on NPR was about Hillary Clinton and Barrack Obama, and how..." "Mom? When you die, does your skeleton stay all together, or does it get scattered everywhere?" (And of course I immediately get an image of a bomb detonating in a crowd) "Ummm, I guess it depends on *how* you die, hon, but it almost always all stays together in your body... etc.
One last thing - a few months ago, we went to see Mr. Magorium's Wonder Emporium, and we invited a little friend and her mom. The movie starts out talking about how Mr. Magorium is over 200 years old, and that he is on his last pair of shoes, and when these shoes wear out, he will be ready to move on, but he needs to make sure he has someone to take his place and run the magic toy store. It seemed to me a very gentle introduction for young children, and Mr. Magorium had a very healthy perspective of his imminent demise. But I was worried that the other mom I had invited wasn't ready to tackle the subject with her 4-year-old, but she said her daughter really liked it and that it fit in very well with the girl's own ideas of life and death, the circle of life, and things like that. So you may want to give that a spin. I can't think of a gentler way to bring up the subject of death with a young child. (And MY kid - who has been talking about death a lot 6 months earlier, took the whole thing in stride - he didn't talk at ALL about Mr. Magorium passing on. All he talked about was the silly stuff in the movie - the pet giraffe, the magic toys, and when the toy store threw a temper tantrum - he LOVED that part.)
The Lion King also talks a *little* about "The Circle of Life" (the cub loses his father, though) and, of course, there is the classic book "The Fall of Freddie the Leaf".
There are lots of other books about talking to children about death, if you want to. You have to know your kid and decide what she can handle, and whether you want to bring up the subject at all.