Can young babies tell the difference between humans and household pets?

wow good question?
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Even very young infants show preference for human faces over other shapes and images.

By the time your baby is 4.5 months old, she definitely knows the difference between people and animals, but it sounds like she really loves your puppy, so that's fantastic!
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I think they do, although sometimes I swear my 22 month old thinks his baby brother is a dog =))
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I would say that a baby that young has no clue about 'species' as older children might catch on to. I think that your baby knows that you are 'Mom' - the one that mostly cares for her, feeds her and comforts her. I think too that she knows who 'Dad' is - the other smell that comforts and cares for her (and potentially feeds her). I doubt that she will consciously think about the differences between your dog and her parents - other than the dog is fun but doesn't necessarily feed her. She likely sees your dog as a 'familiar presence' and something that comforts her (my dog hones in on crying kids and goes to 'their aid' - whether we humans like it or not, so i am assuming your dog does something similar).
Species doesn't enter as a concept but familiarity does. Your dog is familiar and comforting, just like you and your husband are. Your dog likely tickles and plays gently, which causes her to have fun.

I am not sure if that makes sense but it's hard to describe.
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As far as small children are concerned, everything they see belongs to them, and anything that reacts to them in a positive way has got to be good. Personally, i dont really think that that sort of concept is understood by babies, what they are isnt really important to a baby.
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My son is 9 months old and since he was able to roll over and reach out to my puppy. She is just over a year old. I got her when I was pregnant. And evertime I would put her either beside me or she would sit on me he would kick her. She didn't know what was going on. But since he was born she was curious. And at about three months when he started to roll and reach out to her. You really can't keep them apart. Its HIS doggie. He loves his puppy. Yesterday he was in his exersaucer. And could care less about his toys..he was was trying to play with the puppy..it was adorable…I got a pic…they play tag…its so cute..she will lick him and then run and..he will crawl to her and play for a min then crawl away..they do it for almost 10 mins at a time…I think its cute..they know the difference..
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About 4 months is when my baby really started to get into our dogs (two chihuahuas) She hadn't shown much interest before then. And she developed her own communication with them (or at least she attempts) We say that she is "barking" at them because she makes a noise that closley mimics their barking and she only does it at dogs (or my parents cat)

I do think they realize there is a difference between humans and animals because she only "barks" when she sees animals, she doesn't "bark" at humans.
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