Have you synced you Kobo to your library after purchasing the E-book?
You won't ever be able to put the book into Calibre because it has DRM (Digital Rights Management) and will only work with programs with ADE.
Don't worry about downloading a book from the library, If you have Google Chrome (The best web browser
) it will show up as downloaded at the bottom of the screen and then you open ADE and drag the downloaded file into it, it may take a couple of seconds for it to show up in ADE but it will be there. Hope this solves you problem