This was an interesting question I was asked recently about animals. It all comes down to the understanding of who we are and the relation we have with animals.. People can sometimes get confused with the aspects of human and animals and forget we are the same as well.. Before we go much further, Humans are animals!
All life has energy whether it be a tree, a frog, a dog, you name it, this energy is called the Spirit.. Whether that energy is same or not for other animals, that is for own personal beliefs, however from my own opinion all energy or spirits is equal.. The only difference between the human spirit and animals is the power of the mind during life here..
The mind is a powerful tool, it creates all sorts of effects to the spirit and can disable us even on death.. Animals can let go well upon death and tend to leave to the after life yet the way the mind is conditioned in humans we learn to cling to life.. In a way ghosts is the clinging concept that lingers and that is why most ghost experiences is with human ghosts only..
So back to my point on whether an Animal has a Spirit, I say yes we all do.. They have there own spirit experience here on earth as well.. Just like we all do..