Copying passwords to the clipboard is dangerous, because it potentially exposes them to every running app!
Some possible solutions:
The Android platform offers the ability for 1Password to act as an Input Device, which would allow the use to direct 1Password to directly inject passwords into the username/password widget. Granted, I haven't fully gone through whether the APIs allow for a pleasant experience (i.e one that doesn't disrupt the user's default choice of keyboard or place pesky persistent notifications).
At the very least you could use ClipboardManager to blank out the clipboard after a sane fixed interval, or place a notification allowing the clipboard to be cleared when the user is ready.
Thanks! App is looking much better. Thanks for taking the platform seriously.