The other night we went to a friend's house, a place new to Cora, where she met six dogs for the first time. For the first two hours we were inside with just one, a large calm doberman, who Cora patted a few times but otherwise they ignored each other. Later, the rest of the dogs were let inside and a 9-month-old malinois ran up to Cora and greeted her very excited and roughly, nearly knocking her down and it was obvious from her face she was overwhelmed. The interaction only lasted a few seconds before I scooped her up, and by no means was she upset enough to cry or yell or do anything more than frown.
Over the next few minutes the other dogs came to say hi while Cora was in the safety of my lap, including a second (calmer adult) malinois who looks very similar to the first. Similar enough that I would have assumed a baby could not tell them apart after only just meeting them, but she treated the two very differently: for the rest of our visit, if any of the dogs brought their heads within reach, she would attempt to pet them, except for the puppy. She wanted nothing to do with him, if he tried to sniff her, even if it was polite this time, she had a very strong negative reaction, saying "no, no" (well, more accurately, "doh, doh") and emphatically waving her "stop hands" at him (the way she reacts to food she doesn't want, or a person she doesn't want to hold her). But later, when the puppy had been put away and Cora was back on the floor, she happily sought out interaction with the adult malenvois and two other smaller dogs she'd just me.
There's been some study on if and when babies can tell apart animals, but it's mostly been about monkeys.
15-month-olds can be very judgy, as I'm sure other parents can attest.