While animals do not have "souls" in the sense that humans have (whereby via the soul one can have a conscious relationship with God) all living things have God's life essence and live on in God just as saved humans do.
If arguing about this with selective Bible quoters check out Psalm 35(36): 7, in previous blogging to this one, where "man and beast you save, O Lord" is stated.
All animals and plant life force is preserved and is the "scenery" of heaven. This is why the Qur'an and the Bible (Revelations) accurately describe heaven as a garden. All animals and living matter are "saved" because they are incapable of and innocent of sin. So yes, your child will see Fido in heaven.