The movie was released in 1989. It is a cute title, and loving dogs myself, and guessing they cannot sin, I have no problem with the premise. Theologically I have no proof, and so the bottom line is I have to say absolutely positively for sure, I don’t know whether all dogs go to heaven or not. But I am pretty sure that all cats go to the other place.
But what is true or not true about dogs and cats is not the same for humans. The Bible teaches that we have indeed all sinned and come sort of God’s glory. It is also equally clear that the payment our sins earn is spiritual death. And it is not so much the issue of how big or small our sin is, it is the fact that we have sinned against an infinitely Holy God. It is who we have sinned against that necessitates such an extreme penalty for sin, not the volume or heinous nature of the sin itself.
God, however, is overflowing with abundant kindness and absolute mercy and grace. So He determined to pay the penalty of sin in our behalf through the death of Christ on the cross. He offers forgiveness for our sins and the opportunity of new life to all who will receive it. John 1:12, “As many as received Him, to them He gave eternal life, even to those who believe in His name.”
Your dog is not capable (in my humble but accurate opinion) of moral choice. Your cat, however, it is just demonic. You and me, we are sinners in need of God’s grace.