How relevant was the death of the dog? Was she very fond of it, and did it play a large part in her life?
There are so many things in modern life that a young child cannot understand or comprehend, even though they may make use of them, such as TV, mobile phones, computers etc.
Even things in the media that are intended for children have, in recent years, got increasingly dramatic, violent, and possibly inappropriate.
I would guess that she is probably intelligent, and thinks deeply and creatively about things that could seem, to her, potential hazards, and doesn't know how she could confront or cope with them.
If possible, I would avoid all TV while she is around to see or hear it, and even avoid stories that have any degree of threat in them. I worked with primary age children for twenty-five years, as TA or voluntary helper, and there are many things that can confuse, unsettle, annoy or worry children, that adults cannot see any rational explanation for.
When our DS was four and we were on holiday in the Lake District, I made the mistake of telling him that the mountain we were on had, many millions of years ago been a volcano, and he became worried in case it could erupt again.
Conversely, things that could be dangerous may not be understood by a child. Taking him to school by car, we were waiting to turn right across oncoming traffic on a country main road and I commented on how long it was taking for there to be a suitable gap. He said: Yes, we don't want to crash, it would scratch the paint!