The dog has no idea of object constancy.
How often do I deny God's constancy in my life? "You haven't done enough for me today!" "You're not there for me!" "You won't give me what I need!" "I'm not going anywhere with my life!" Fear runs rampant when I let it.
Yet God says, "Fear not!" He says, "I am always with you." He says that He will give us what we need; that He will give us things that are good for us; that He has plans for our lives. He says, "Don't worry." He says, "My ways are not your ways."
There is no fear in love. How about if I try trust instead?
"We need have no fear of someone who loves us perfectly; his perfect love for us eliminates all dread of what he might do to us. If we are afraid, it is for fear of what he might do to us and shows that we are not fully convinced that he really loves us." [1 John 4:18 (Living Bible)]