A.B.
So sorry for your loss. My dog died two months ago, and my 4 yr old still asks about her death and cries. We have a new dog, but it doesn't change our loss. There's a lot for them to process and grieve; they didn't see this coming the way that we as adults do. To them, it's a total shock. My daugher also started applying the concept of death to people and became very scared of losing me. Your little one may also be terrified of losing you. The main thing that's helped has been telling her that our dog is in heaven and is able to run, play and eat again. Besides that, it's acknowledging her grief, empathizing that I also miss our dog, answering questions (including ones that I think she has but that are unasked) and providing lots of love and cuddles.
My pediatrician gave me a list of books to help children (and adults) deal with pet death. Some on the list for 3 - 8 yr olds: Lifetimes (Bryan Mellonie 1983), A Funeral For Whiskers (Lawrence Balter, 1991), Barn Kitty (june Kirkpatrick, 1999), I'll Always Love You (HansWilhelm, 1985), My Pet Died (Rachel Baile 1997), Remember Rafferty: A Book About Death of a Pet for CHildren of All Ages (Joy Johnson, 1998). One for Adults is: Pet Loss: A Thoughtful Guide for Adults and Children (Herbert A Nieburg, 1906).