Yes... All animals have a soul.
Man also has a soul.
But, the difference?
Man's soul was created in the image of God.
Animal souls were created generic in nature.
That is why God was able to give us animals for food.
Then God said, “Let us make mankind in our image, in our likeness,
so that they may rule over the fish in the sea and the birds in the sky,
over the livestock and all the wild animals, and over all the creatures
that move along the ground.”
So God created mankind in his own image,
in the image of God he created them;
male and female he created them." Genesis 1:26-27
Man's soul was created in Chapter One before the body came into existence in the second chapter of Genesis.........