The Catholic Church (to which I also belong) certainly draws very sharp distinctions between the nature of the human soul and animals, but never really states that animals don't go to heaven.
IMHO, Revelation 5:11-13 pretty much convinces me that they do.
Yes, there are many scriptures which point to animals being in Heaven — too many to list here, but there are some great books which go through them: Jack Wintz’ books being my favorite so far. Many of the great Christian apologists from centuries past took it for granted, based on Scripture. I consider it a sign of the times and the growth of the human ego among those who should know better that it’s even a matter of dispute.
I just read Rev:9-11 and I am pretty sure the “Lamb” it refers to is Jesus but never mind, my dogs are going into the ground with me. The ashes of the ones who are gone are waiting in jars on the book shelf for that day. I hope and pray that they all end up in Heaven with me.