@maxdog,
Soul is something whose knowledge is only with God. Some one asked the same question to Prophet Muhammad PBUH and in response Allah revealed following verse of the Quran:
And they ask you, [O Muhammad], about the soul. Say, "The soul is of the affair of my Lord. And mankind have not been given of knowledge except a little." [Quran 17:85]
Today we have made so much progress in science and still we could not understand the reality of soul. We know when a person dies, his/her soul leaves the body but no one has seen it. That's how the matters of unseen are in this world. We don't have eyes to see the reality. But in Hereafter we can see all unseen.
Regarding your question about animals yes they do have souls. And they will also be gathered on the day of Judgement. Quran says:
Quote:There is not a moving (living) creature on earth, nor a bird that flies with its two wings, but are communities like you. We have neglected nothing in the Book, then unto their Lord they (all) shall be gathered [Quran 6:38]
All creatures will be gathered on the Day of Resurrection, animals, beasts, birds and everything. Then Allah’s justice on that day will reach such an extent that Allah will settle the score for the hornless animal with the horned one. Then He will say, ‘Be dust,’ at which point the disbeliever will say:
Quote:Would that I were dust!’[Quran 78:40]