I am sorry that the puppy did not survive. Your baby is lucky to have you to comfort her on her loss. When my Lily lost her first born the umbilical cord came out first followed by the pups feet. Was the brown goo that you saw possibly the umbilical cord? The pup that Lily lost was only 2.25 oz. It wasn't too big to pass through her, (She is just over 4 lbs.) but it was in the birth canal too long. I hope that Mama is doing better.
