I am sorry to hear about your pet. I have lost a few too so I know how you must be feeling.

I have read that people who die in accidents are confused, sometimes they do not know they are dead even. They need some time to adjust and rest as do people who have died natural deaths. Seems logical after living on this planet.
Why should it be different for animals?

I once came across one NDE story which related how the woman was met by a dear pet that had passed on. The dog showed her around. In her NDE animals go to a place across "the rainbow bridge."