To create worry humans elongate fear with anticipation and memory, expand it in imagination and fuel it with emotion. The uniquely human mental process called worrying depends upon having a brain that can reason, remember, reflect, feel, and imagine. Only humans have a brain big enough to do this simultaneously and do it well.
I think the idea that death is not the end, that your dog's just gone to live on the farm, is limiting. Thoughts like that prevent you from making the most of the time that you have.