A simple way to do this is to swap the server files in the one-click install image of Django that Digital Ocean provides with the files you've created on your local machine.
However this would only work if both projects use the same Django version, the one-click image I believe is using 1.6.1, and if you've started a project recently it is likely you are using a version > 1.7.
If you are using the same version though, just replace the django directory with your nearly identical project using git, filezilla, or a similar program. Then modify the settings.py file to match that of the original settings.py, mainly the credentials for the database. Then issue a 'python manage.py sql <your apps>', 'python manage.py syncdb', and 'service gunicorn restart', and you should be good to go.
Again this is only a working solution if the versions match, and its an imperfect one at that. If you're new to Django I'd suggest reading up on Django settings and configurations, which should allow you to deploy applications on nearly any VPS.