What should you do?
I don't have a scientifically proven answer - I just can tell you my experience, as we already have had many such conversations (even at an early age).
I think you should talk as openly as possible (and necessary) about death to her and you should show her (if possible) that it makes no sense to be afraid of death as it is (partly) beyond your control.
Our son started at 3.5 years old to worry about death, often stating that he did not want to die or that he did not want us (his parents) to die, as he does not want to be left "alone".
(It began when he asked for his grand-grandparents, who died some years ago and whom he saw (with himself as a baby) on photos.)
He had some short phases where he was talking about death at least once or even several times a day. This was very, very touching and difficult for me.
What to say? I told him that we'll take care of ourselves as well as possible and that I hope we'll all live for a very long time.
He said he wanted us to die after him - then I told him that mostly the parents die when their kids are already quite old and have their own families and children, so I hope he'll understand that this is typically quite far away from now.
He also had phases where it seemed to be interesting or even fascinating for him to "make" something (mostly animals) "dead" - this stopped quickly, fortunately. I explained to him that the smallest animals, just like himself, do want to live.
Are the 2 events correlated? Most probably yes, but from your description it was your daughter who began making death a topic by letting her doll being dead.
Did you ask her first if she knows what "being dead" means or was your explanation the instantaneous reaction to her play?
(In the latter case I'd consider it a bit hard, but asking if the child understands the words she used and then explaining or adding - where necessary and considering the child's age and "maturity" - what it really means, is absolutely appropriate IMHO.)
Has she ever had experience with death before (dead animals, dead relatives or acquaintances)?