The Bible isn't big on telling us what heaven's like. The word picture in Revelation 21 often used to describe heaven actually describes the new earth and the new Jerusalem. So says scripture. These animals are shown as a part of heaven's realm, so it seems likely, since they have souls, that heaven is also the eternal home for those animals that have been an important part of creation from the beginning. Because, unlike animals, humans can choose to do evil.
Animals can only choose to be animals.
Animals are heaven bound. The real question is . . .