I think it really depends on what we mean by a soul. All creation is a part of God in some sense, as God willed it all into being. It all serves his divine order. All Living things also die, including humans. So in order to deal with this existential angst we like to conjure up images of an afterlife modelled after high class living for the society of the time. For the Feudal Europeans this was a heavenly court like their own Kings and Queens. For the Muslims, it was like the palace of a rich sultan complete with harems and gardens flowing with water.
Personally I think both are off base, and from my own reading into various theological philosophies I think the most glaring mistake in all of them is in God's first command. "Be Fruitful and Multiply". People focus on the basic mechanics. God wants all life to increase. Okay. But its the "Why" that really matters. At a fundamental level god wants people to see his creation. Even modern physics notes this fact. Quantum mechanics functions differently when its being observed as opposed to when its not. The more living things there are, the more observers of creation there are.
So in this respect, Animals do have a place in gods heavenly chorus because they are observers just like us. The difference I think is that humans are aware of their observation. Which means we are capable of willful blindness, or even lying about what we see. We are capable of forcing creation to contort into something it was never intended simply by will of our ability to delude ourselves. Something no Animal is capable of doing.
This is the essence of the verse saying "God made us in his image". We aren't just casual observers of creation. We are ACTIVE participants in the creation. And the promise for us is different then with the animals. We have a higher purpose, and that purpose could be turned to corrupt ends. So we are tested, and those found unable to handle the responsibility of being an active creator, those who would turn their thoughts and words to destruction cannot come into their own as active participants in Gods plan.
Oddly enough, it was the video game "Outer Wilds" that really captured my own personal "revelations" as it were. It was rather shocking to me that someone else had hit upon the same idea because I figured I was completely schizo. Apparently I am in good company.