IMO, it is not a good idea to make her write down more steps. She could grow up to write a graduate math textbook. Flip through one of those--there are hardly any explanations there because they assume by that stage the reader can fill in on their own.
Sorry, but I literally LOLed at this. The people who write graduate maths textbooks are (typically) academics, who spend a fair proportion of their time teaching undergraduates. Believe me, they have to be capable of giving very full explanations when occasion demands, too!
I agree with Val; it sounds as though your DD may have two problems - if she's underchallenged, learning to show her work isn't going to help that - but learning to give detailed explanations is important. One thing that has helped my DS with this is a very simple re-presentation: not as "show your work", which seems pointless if his work is securely in his head, but as "explain how you did it", i.e. given enough information that someone who'd looked at the question and didn't understand how to do it could learn from your explanation. This is also useful because it opens conversation about what to assume about your reader; he has to explain at different levels in different circumstances. In a few circumstances he's expected to, for example, show every line of algebraic working as he rearranges a formula ("explain this so that any of your classmates could follow the explanation") while in others that would be completely inappropriate and only key insights need to be explained ("explain so that if you'd read the explanation before you'd really thought about the question, you'd have understood it straight away").
