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I am a Christian priest (Anglican) and I get asked this kind of stuff in real life, quite a lot. It saddens me deeply that such questions even need to be asked; there is so much rubbish taught in the name of Christ by churches and individuals that claim to know too much more than they actually do.
Many years ago I was asked by a high school student to pray for her dog which had just died. The school chaplain had refused on the usual grounds (as stated by some of the answers on here) but I decided that, not having any idea what would happen to a dog that had died, other than its body being buried in the backyard – is there anything left of the dog after death? But the relationship with her human friend was important, and the state of the human friend’s emotions were important, so I prayed for the dog, and for the girl, and she was happy. That seemed to me to be sufficient.
But punishment? Hell? Not on the part of the God I know and love. Not for the animal, not for the girl. “God is love” is said twice in the Bible – twice in the same chapter, so we don’t too easily forget. Seems we forget anyway. That love, of which I know just a hint, the whisper of God’s eternal song, takes me into the realm of mystery but in so doing does not take away the essential nature of love: care, vulnerability, goodwill, and God is eternal so that care, vulnerability and goodwill extend infinitely.
Is there a hell for any creatures?
The bible does not, contrary to popular opinion, teach that there is. There is Gehenna (often mistranslated “hell”) which was the rubbish dump outside Jerusalem in Jesus’ day – and was the dump because centuries before the prophet Jeremiah had declared that, as out was used for child sacrifice, it was unfit for any better purpose. Jesus used Gehenna as a metaphor for destruction, the place where the fire doesn’t go out (as in most rubbish dumps) and the worm never dies (as in most rubbish dumps). He used many metaphors and for some weird reason people don’t see his humour, his exaggeration, but think he meant everything in this literal way that nobody uses language ever. There is the lake of fire, mentioned in Revelation 20 and nowhere else; it too is a metaphor, a symbol like everything else in the Book of Revelation, and it refers to the destruction of – wait for it – all the powers that destroy the earth and its inhabitants.
It is the annihilation of evil, no more and no less.
Peter Llewellyn – https://www.quora.com/Does-God-send-animals-to-hell