Many toddlers go through an aggressive phase, and it's more about their personality than how they're parented. Unfortunately, GD won't create toddlers who don't react to frustration this way. Some kids don't, but then some kids who are not parented with GD also don't have aggressive phases.
My first suggestion is to phrase whatever you say in a positive rather than a negative. Contractions are a bit more advanced than other language, so kids will sometimes hear "don't hit the cat" as "blah hit the cat." Even if they understand "don't", they still end up with the image of hitting the cat in their head, and toddlers - especially as young as 19 months - have very little to no impulse control.
"We don't X" is even tricky, because if you think about it very literally (and young children are super literal) then if she just did it, yes "we" do X. Think about it from her point of view. She hits the cat, you say, "we don't hit the cat" but she just hit the cat so it's literally incorrect.
I would instead say something like, "Be gentle." Or even just "gentle." "Nice" isn't very specific, and is more of an overall impression than a behavior. Like she might think, "Well I am nice." She's a nice girl, right? And people probably tell her that she is a nice girl. So she probably associates that with her all the time rather than with any behavior. But "gentle" means something very specific and is very much associated with behavior.
OK well that got really long but all I really did at that age was if they hit someone to gently hold their hand and say, "gentle." Over and over again, trying to catch every single incident, so that I was consistent. And they did both outgrow their aggressive phases pretty quickly. It lasted longer with the one who talked later. As their language improves and they're able to feel heard and talk about how angry they are more and more, they generally get aggressive less and less. You said her language is good, so hopefully she'll get past this early.
Which leads to one other thing. You can talk about emotions and feelings, as having names for how they're feeling sometimes helps. "You seem very angry." Or, "You're angry that you can't have X right now." Naming feelings, and feeling heard and empathized with sometimes can help as well.