I think if I was a cat, lamb or bird I wouldn't have dominion, but me not having dominion wouldn't necessarily change my soul or spirit. (You can't SEE spirit, it's invisible, it doesn't have an image).
There is the scripture that says God cares for the sparrows. Not one of them falls without his knowledge. So if the sparrows have a relationship with their creator, then every other creature He created must have as well.
If I were me in an animal, I would be an American eagle. Does anyone know the power of this God created animal?
In Matthew 6:26, 26 Look at the birds of the air: they neither sow nor reap nor gather into barns, and yet your heavenly Father feeds them. Are you not of more value than they? - ESV
I do feel God can communicate with animals like the birds, lions, lambs and even kiwis. How about when a mother bird needs to feed her chicks? How about when a dolphin rescues a human trapped in the ocean? How about when a jungle cat befriends a baby chimp? Could it be that God communicates animal circumstances?
I do believe as man has dominion over all animals it's our responsibility to care and love animals.
But again, I don't believe animals possess the Spirit/soul of God nor will they be resurrected. As you said, "You can't SEE spirit, it's invisible, it doesn't have an image."
That is a good point, Lanolin, however, whether in our personal belief the Scriptures says an animal has a spirit/soul, I don't feel any of us will ever know for sure until we meet our Maker.
It is interesting when we can share whatever the Lord is teaching or leading us in our growing faith.
God bless you, sister.