There’s no actual “duplicate page” feature right now, but what you can try is to use the selection tool to select everything on the page, then go to Edit->Copy. Next, navigate to the new book, but you have to do this in the same browser window, without reloading, or typing in a new URL. So it might be a bit tricky. Once you’re in the new book, go to a blank page, and select Edit->Paste.
We do plan to add a feature to easily copy pages between books, but unfortunately I can’t give any estimates on when it will be complete.
Thanks.