I start by saying that I am no expert here BUT I can tell you what we did when we brought our daughter home. DH had a blanket that Payton carried with him for 2 days. When we got home my DH carried the baby and I walked in alone to pet and be welcomed by the dog who missed me. We did keep him on a lead as he tends to get over excited and though I didn't have a c-section I was not in any condition for the zoomies....

Then we just went on with our lives. Payton was allowed to smell Isabella and then he walked away. Personaly I think not making a big deal out of it was a plus for us. We NEVER left the 2 of them alone in the room together and to this day follow that rule. We did ask him where his baby was and he would look for her sniff her head and then walk away.
Congratulations on the baby! You do realize that as a member of this forum you must post pics of her right