I second Lauren's take on this and would personally exclude animals from this – I think it hits home more when it's a member of your own species.

The wiki page has a lot on Harry not seeing the thestrals despite being present as a baby when his parents died, which could just be authorial inconsistency re: thestrals being an invention in her later books, but I like the idea of it being more "grasping" the concept of death as well as seeing it happen before your eyes.