Of course they do...I mean I don't have actual proof but if they can feel many of the same emotions as humans can then what's to say they don't have a furry little soul that heads into the afterlife?
I'd like to think all my deceased pets are waiting for me up in heaven actually. =3
And for any neighsayers I dare you to watch Hachi: A Dog's Tale and then tell me animals don't have souls and feelings.
...that movie made me cry so much it was ridiculous. The ending is so sad.