P.W.
I could be wrong but I'm guessing that she doesn't actually remember her father or the actual event of his death (or disappearance, as she would perceive it), since she was only 18 months at the time. She will always carry the loss within her as a part of her spirit and personality, however. It seems that her questions and feelings are primarily in response to the questions of her schoolmates, as well as a sense that she is different in not having a father.
I don't think she's too young to understand at 4; it sounds as if you are explaining it pretty well, maybe you need to add, in an age-appropriate fashion, that he died. The advice from the other mothers should be helpful, especially the books they have recommended. I think helping her to talk about how she feels about her father being gone would be a really good idea. After that you could occasionally tell her a story about her father. She would like that. I wouldn't discuss it all the time, as I don't think it's a loss she needs to carry around with her constantly - you can create MORE sadness and sense of loss by constantly talking about it.
I lost my 3 year old brother when I was 5, and I distinctly remember my mother walking in the door and saying, "Hunter died." Believe me I knew what that meant. To tell you the truth it was not the bluntness of how she put it that was the problem, it was not involving me in his illness before he died and never discussing him afterward.
So be truthful without being graphic, and talk about her father with her when you can see she needs it.