K.P.
This can be quite difficult for a young child- When my daughter was 3 we had to have our cat out to slep due to severe medical issues with her. First off, we never used the word "sick" out our cat. We were afraid that my kids would relate their everyday "sicknesses" to mean "going to Heaven". So, we said things like "the cat has an illness" or the "cat has a disease". These weren't words that we regularly used so we felt confortable that the kids would not relate their minor colds with death. Next, we explained that our cat went to be with God in Heaven. Now, in hindsight, that has been difficult, since my kids sometimes ask if they can go see God- but that is likely as a result of any religious conversations we might have. My daughter (and younger son) really dealt well with the death- but we talked about it alot with them. Good luck and my sympathies.
K.