If you had a close connection with your pet dog, such as letting it sleep on your bed every night, caring for it when it was sick and walking and feeding it every day, your beloved pet is bound to have left an impression on you.
Dreaming about animals usually relates to basic or instinctual feelings, behaviours and reactions that may have been repressed or overlooked. Animals have very simple needs and desires and sometimes this can be reflected in their manifestation because you crave or value the same basic yearnings.
Dogs represent friendship, loyalty, protection, intuition, fidelity and generosity as these are all the aspects of personality we associate with such an animal.
The dog might be a representation of you and these qualities which will see you well in your future and help you to succeed because they are desired and attractive traits.
It could also mean that you never really got over their death- in which case it might help you to talk to a friend or family member about how much you miss them. If you can express these emotions while you are awake then you might find you dream about your dog less and less because you have found an outlet to release your true feelings rather than letting them out at bedtime.