Dreams/astral experiences are just as real as walking and living in
this/earth reality. You have an astral body, just like the physical body
that you use to travel the astral - and so do animals who are every bit a much
spirit as you are.
I see this as your dog's way of saying goodbye and it is probably physically
dead. I have had similar experiences with relatives, a grandmother for
example who a couple of days before the death of her physical body met me and in
a dream and said goodbye. She was very happy and dressed in her Sunday
finest and was completely radiant.
You can also meet friends and relatives after they are "gone" and
what is happening is that you are completing cycles with them. This too
happens to me, often.