depressing... but i dont think it is your dog. the necklace could represent your dog, to you, however, it is not possible, to my knowledge, for spirits to manifest in inanimate objects. Now this doesnt mean that your dog's soul may have attached itself to the necklace, but i dont think the necklace is your dog.
when i first read your post, i was confused. hope i answered the question you are trying to convey...?