My dd1 was like this. To the point I used to dread anyone mentioning anything about death or someone who had died just in case she asked about them now, and I had to say they had died because it would start a whole series of questions and worries.
Then this year dd2 was stillborn at 40+5 (dd1 was 5) and I have learned a lot since then.
My advice: if you can, get a little pet with a short life expectancy. Luckily a few weeks before dd2 died, the hamster died (well not luckily but you know what I mean) it gave the dc's and experiance of death and grief in a safe envioronment. They saw the little body and buried it in a way that they wanted. It helped massively when it came to dealing with the death of their tiny and much waited for sister. They had had months of playing with her in my tummy and had bonded so well.
When dd2 died they all chose to see and hold her and coped remarkably well, same with the funeral. In the funeral home, just before we left, they had to put the lid on her little coffin and screw it down. I was finding the prospect upsetting, as you can imagine, but I was also very worried for them. The funeral director came and explained to them what they were going to do, and why in a very honest manner, then asked the children if they would like to help. They jumped at the chance!
Two weeks later the fish died and I felt like I was going to make their little worlds cave in by bringing another death into our lives. I told them honestly and simply that the fish had died and gave them a choice between burial and flushing and the children decided to flush the fish, and after all of the trauma we had been through almost was a little bit funny.
The biggest lesson that I have learnt through advice from professionals etc is to be very honest. We all die when our bodies stop working. Mostly that happens when we are very old, but sometimes it happens to young people too if they are very ill or have been badly hurt. When we die we don't need our bodies anymore so we return them to the ground (burial) or the air (cremation) and our souls, stick to what you believe in your family. I was advised that children are much more frightened of the things they make up in their minds when they try to fill in the gaps. I was advised not to tell them 'not to worry' becuase they will and if you have asked them not to, then they'll just stop confiding in you when the need comfort becuase you have already told them not to.
There are lots of lovely children's books which deal with death Badgers Parting Gift was one that comes to mind and Always and Forever. Both are lovely and give the message that even when the body is gone, the spirit lives on through the lovely memories we have of them and what they have taught us.
I hope it helps, and your little one becomes less consumed with worry. Despite all we have been through the past year, I think dd1 is less worried now than she was this time last year. She still has her moments but they tend to be more sadness about her baby sister than anything else 