It is very common for a person after loosing a loved one, it could be either human or animal, to have dreams about them reguarly shortly after the death, or in some cases to have them appear in dreams perhaps months or even years after thier death.
This can occur for many different reasons and thier are several possible explinations for why this might occur.
Of course the most obvious reason is simply out of grief and remebering the lost loved one, becasue the death can create such a powerful emotion, it is not surprising that this emotion will follow us into are dreams.
It can also be a way to still be with the person or beloved pet after they are gone, when thier soul has moved on in your dreams, you can see them the way you remeber them, and feel thier presence as if they are still there with you.
Or it can be a way for your mind to process feelings and emotions that your concious mind cannot completely process becfasue it is too painful and difficult to deal with. Dreaming of a past loved one can be part of the healing and greiving process and perhaps even give extra clousure that you do not feel you have in the waking realm.
It gives you an oppertunity to say things to them you might wished you had but never had the chance to while they were still alive, or to have one last moment with them, and to properly say goodbye if they died before you had a chance to.
It is also commonly beleived that the dreams of a loved one whom has passed is thier way of sending you a message. The message can be anything, it can simply be to let you know that they are happen and safe where thier soul is now, or in some cases they can appear to you to help guide you through a difficult time, or to give you a warning for something that is to come.