This is a common question that people usually ask. I like the answer that Got Questions? features:
Answer: The Bible does not give any explicit teaching on whether pets/animals have “souls” or whether pets/animals will be in heaven. However, we can use general biblical principles to develop some clarity on the subject. The Bible states that both man (Genesis 2:7) and animals (Genesis 1:30; 6:17; 7:15, 22) have the breath of life. The primary difference between human beings and animals is that humanity is made in the image and likeness of God (Genesis 1:26-27), while animals are not. Being made in the image and likeness of God means that human beings are like God, capable of spirituality, with mind, emotion, and will, and they have a part of their being that continues after death. If pets/animals do have a “soul” or immaterial aspect, it must therefore be of a different and lesser “quality.” This difference possibly means that pet/animal “souls” do not continue in existence after death. …Read More!