I think for most animals it depends on a ton of things. I was told (since after our last child, the dog was new to the family and neither of us had owned a dog in a very long time), to le the dog sniff and/or have one of the child's baby blankets, so the dog can figure out who the other "thing" in the house is.
We have had cats (mostly all cats) and the same dog, all the animals love the kiddo, even the cat when her tail gets pulled sometimes. |