For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
If my pet Dog, 'Teddybear', is not in Heaven when I get there, it will not feel like heaven to me and I will be immensely sad. As heaven is said to be a joyful place, with no tears, pain or sadness, then for me, at least, 'Teddybear' my Dog will be there to greet me; probably being led by the LORD.
I was born in Italy and I live in Britain. In Italy animals do not have souls, in Britain some people believe animals go walking over the rainbow bridge after death. Reading Isaiah the animals present during the Millennial Kingdom are different from the ones we know, the lion will be eating straw with the lamb. So I think that the animals that will be present will not be scavangers, killers and predators any longer, I think they will be new different animals.
I believe if there will be one type of animal in Heaven then there will be ALL types of animals in Heaven, more specifically our pets. With that said we must refer to Isaiah 11:6-8.
The problem with animals going to heaven is that they are not equipped cognitively to appreciate the joys of heaven. Will animals gain sufficient intelligence to communicate with humans?