According to Support, as soon as you turn off the Easy One-Click Drupal, it will make your database available to you so you can dump your data, or access it with your new Drupal. This should be fairly minor, considering that the Easy Drupal is a very standard configuration.
1) Create your Fully Hosted domain
2) Manually install Drupal
3) Turn off your Easy Drupal (at your own risk, I've never tried this, but Support says your database will become visible to you)
4) Point your new Drupal to your old database.