without knowing to much the context of what you want to do with the '10 other devices', i can already say that this isn't a really good idea to dd the rootfs. while it might (seem to) work, it is very prone to errors.
there are many scripts that run at 'first boot' that wouldn't run in your case, for example.
the right thing to do would be to make your own images and add your packages in that image (which implies that you also need to package your own app as a debian package).
if you can't go that far, you can look into a few tips:
* when you install deb files there are downloaded/copied in /var/cache/apt/archives/, so once you've installed on one board, you just need to copy these files over to the new board (and reinstall them there)
* for your application, it should be safe to tar/untar it over.
this might not be perfect either, but still better than dd'ing the entire rootfs...