no, scene show clearly she do not cry about dog. she cry because her dad angry at her and question her reason for why she kill the dog
even then their point still stand, she's not that much of a psychopath by definition, look it up. i get it, you love dog, i do too, is she crazy for killing that dog? yes. but does that make her a psychopath? not entirely, you see, it's not as simple as, you either a psychopath or you're not, it's a spectrum. im nickpicking cuz i watch a few episodes of MD about it. and because it seem like she still experiences emotions, we cant say she's a complete psychopath YET, "yet" because psychopaths are also really good at faking and lying, even to themself so we dont know if any of this is genuine or not