It's easy to see animals as having souls, especially if you're a pet owner and love your pet. Most Western traditions would tell you they don't, however.
So it basically comes down to your belief structure. Are we somehow seperated from the rest of creation due to some God-figure (Christianity, Judeaism, Islam, etc.) or are we simply part of a greater whole, neither greater nor lesser (primarily Eastern traditions)? And do you believe in a soul at all (Atheism)?
"If we do, so do animals" would be my opinion. But definitions of what a soul consists of outside of Western tradition is a tricky proposition, at best....so it might not be a soul as you would think of it in what I'm assuming is a Christian setting.
There's no way to know so believe whatever makes you happy here. So long as you don't go all PETA and start valuing animal life over human life.
;-)
Of course if you really wanted to be rigorous you'd need to define soul in the first place. If your cat plays the sax he has soul in one way but perhaps not another.