Creating and transferring a site with Django
Of course that's possible and in fact it's the only way to "go live". You don't want to develop in your live server, do you? And it's true for any platform, not just django.
If I understood your question correctly, you need a system to push your development code to live.

Use a version control system: git, svn, mercurial etc.
Identify environment specific code like setting/config files etc. and have separate instances of them for each environment.
Create a testing/staging/PP environment which has live data or live-like data and deploy your code there before pushing it to live.
To avoid any downtime during deployment process, usually a symbolic link is created which points to the existing code folder. When a new release is to be pushed, a new folder is created with new code, after all other dependencies are done (like setting and database changes) and the sym link is pointed to the new folder.
As a fledgling Django developer, I was wondering if it was customary, or indeed possible, to create a site with Django then transfer the complete file structure to a different machine where it would "go live". 
Thanks,
~Caitlin