Dogs do not have souls. Like people they ARE souls.
In the King James Version the Hebrew word translated ‘soul’ is ‘nephesh’.
Adam was made a ‘living soul’
From this we see that body + breath = living soul.
Animals have the same constitution.
The word ‘nephesh’ is used of animals but is translated ‘creature’.
Genesis 1:21 And God created great whales, and every living creature (Hebrew – nephesh) that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.
Genesis 1:24 And God said, Let the earth bring forth the living creature (Hebrew – nephesh) after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.
Genesis 2:19 And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature (Hebrew – nephesh), that was the name thereof.
Soul is the whole being.
Ezekiel 18:20 The soul that sinneth, it shall die…
When we die, our whole being (soul) is placed in the grave.
Psalms 89:48 What man is he that liveth, and shall not see death? shall he deliver his soul (Hebrew – nephesh) from the hand of the grave?
I hope this helps.