I don't think this is very unusual. Children pick up on more things than they communicate. They look, they listen, they try to figure out their world, they stew about it, and they wonder.
I remember when my older son was about that age, and every morning we drove past a derelict drive-in restaurant building. It had been abandoned since we moved to that neighborhood. It was just... there. One day, it wasn't; the building was half-gone, in the process of destruction. I glanced in the rear-view mirror and my son's face had gone white. It hadn't occurred to him that buildings could be taken down. It was such a shock. We talked about it... how buildings were built and un-built, how the building wasn't alive the way he was and taking it down didn't hurt it, how something else would be built on that site and we could watch it go up.
It's really surprising what goes on in children's heads.
I remember, further back, that when I worried about death as a young child, my parents simply told me not to worry. They thought that would comfort me, and maybe it should have. They did the best they knew how, but it didn't help a whole lot.
If your daughter were my daughter, I think I would say, "Yes, I will die some time, and so will you. In this world everything that's alive dies sooner or later. That's the way this world is made. I want you, and myself, to live happily for a very long time, so I try to make us healthy and keep us safe. I will be here for you as long as possible because I want to take care of you. There will *always* be someone to take care of you."
I would also start telling her about the concepts my religion provides - let her know that there is another, better life after this one, and that nothing is random or meaningless.
To my thinking, that sort of answer teaches concepts a child can think about and it can open the door for more - yes! - questions and answers. It also provides a little security to a very young child, to know that she won't be abandoned and that she *can* count on someone being there to take care of her. I bet that's in her mind, even though she may not be verbalizing it.