Though lets take a step back here. I think the real question you have to ask yourself is this: Are you ready for Docker in production?
The technology for running applications within a Docker container has been battle hardened for the last few years. As long as you are packaging and running your app basically unchanged, Docker going work just fine for you. Any problems with Docker you might encounter, are pretty well documented by now. While you aren't taking full advantage of Docker by only running one container on one VM, it will still improve pretty much everything about your development workflow and server management.
Running Docker in this fashion, while 100% viable, is only scratching the surface. It opens the potential for doing many more interesting things with your infrastructure that you couldn't do before. It is this potential, that if not properly implemented is going to cause sorts of havoc that you are not even prepared for. In the future, I will open this can of worms. I can show the potential for these features, the cons, as well as how to mitigate issues you may encounter.
In the meantime, stick to the simplest possible Docker setup. I will posting a simple Docker Rails setup in the future, stay tuned.