I remember having fears of death somewhere between the ages of 3-5 (some of my earliest memories), and again when I was around 11 (a normal stage). And now that I'm in my 60's, it's a common topic/fear among my peers.
To be overwhelmed by fear is probably not normal. If a few calm conversations with your daughter don't help her, she may do better with some counseling.
But I'd like to suggest that you don't try to convince her that her fear is silly, or unfounded, or "that there is nothing to be afraid of," or that "you won't die for a very long time." It's very real for her, and you can't know she won't be hit by a truck tomorrow, and none of those intellectual arguments will reach the place in her emotions where the fear is living. It would be better to give her some calm, supportive listening, and let her talk/cry her way through to some sort of resolution of her own.
Just offer quiet answers to her statements, like "Yes, sweetheart, I hear how worried you are," or "Hmm, I see." Hold her if she wants that. Eventually she will "spend" much of her anxiety, and then you can share your own feelings (admit to fear if you have it so she will see that it's possible to live with it), and share any stories/understandings/spiritual teachings you have about death.
One of the things that helped me the most was realizing that death would take me back to the place I came out of when I was conceived. Since I had no awareness of being afraid before I was born, I wasn't too likely to have fear after I died.