Yes, according to William Bulman, a leading expert on out-of-body experiences. During our out-of-body experiences, people have seen and interacted with animals on numerous occasions.

It is apparent that both people and animals continue to exist after their deaths.  Many people during an OBE (Out of body experience), clearly remember seeing a thin string, or what some may refer to as a "silver cord," pointing from the nonphysical dog toward its physical body.  This rope resembled spiderweb silk in appearance. The end conclusion is that every animal is multidimensional and continues to exist after death, just like we do. Many people have previously lived as animals, as well. 

Some insects and animals have a collective mind. When they leave their lifespan on Earth, whether right away or after some time has passed, they return to a group awareness, which implies they can link to a hive type mind while still in a body. 

When an animal achieves a particular point in their spiritual development, they become true induvials and separate from the communal consciousness, which gives them the ability to grow into other forms of life, including humans.

You should try and encourage spiritual development and individuality in dogs, cats and other pets and animals by consistently showing them sincere affection.