We have a VERY sensitive dog (wants to leave the house if one of the kids starts crying or an adult talks back to an annoying news report), and when I was in labor, he was totally mellow. He actually came and sat on the bed with me, totally of his own accord, when I was in the most intense part of labor. DH was madly scrambling to fill the pool, my sister was upstairs distracting my son, and the midwife was in transit. He was very calm, not freaked out at all, and it increased my already very deep love for him that he came in to be my 'doula'. He was in the room when DS2 was born, and after the birth, he came into the bedroom when the midwives were checking my placenta and checking me for tears (I thanked him and shooed him out at that point because it seemed vaguely unsanitary for him to be up on the bed with me). I bet your pup will be a supporter in the birth process or will ignore it all.