I'm a Christian too, but I don't believe animals have souls. God created all humans in his likeness, and we can do things animals can't. We can love, we can create, we can learn. Sure, you can say animals can love, but not like us, we love selflessly. Animals love you for the things YOU GIVE them, not just for you. Animals create on instinct. You don't see a bunch of monkeys go out and build a skyscraper. Animals can learn, but not nearly as advanced as us. Guinea pigs can learn to turn circles, but they can't learn fractions. Animals weren't created in God's image, therefore they can't have souls. Only we have souls. When animals die, there're gone. Forever. Believe me, I've had animals that I loved die, I know it makes the pain easier to bear if you think he/she is still alive and happy somewhere. But that's just fantasy.
You may think it isn't fair. Why should you live forever (if you have accepted Jesus as your Lord and Savior) and not your pets? The answer: man brought sin upon itself In the Garden of Eden. Adam and Eve yielded to sin and ate from the Tree of Good and Evil, even though God had forbade them to (Genesis 3). Our punishment is to die. If we didn't disobey God, then people and animals alike would live forever.
@Guinea Pigs 'n Things, you said animals have more soul than people. That's wrong, because animals can't sin, they can't talk. If your pet could talk there would definitely be arguments.
@Betsy, you asked how animals could live if they don't have souls. They live because they have a beating heart, food, etc. (I know that was a rhetorical question.)
I do believe though that there will be creatures in heaven that remind you of your pet on earth.