It's good to always be calm; being calm has a reward, and you've earned it. There's one thing I always tell myself: being calm pays off a lot. I strive to remain calm and avoid finding myself in situations where I get angry and say things I'll regret later; being calm helps the mind.
When it comes to kids, parents need to be calm and not too quick to pass judgment on them when they're wrong. See how she came to you herself to teach her. I really love that part with your daughter; she is a good kid.