Create A RDS Within Elastic Beanstalk or Separately?

You can create a RDS within an environment using Elastic Beanstalk, however:

Once added to an environment it can't be removed.
It will be tied to the lifecycle of your environment, so will be lost if the environment is closed.

For a production environment its often better to launch a database instance outside of your environment and configure your application to connect to it outside of the functionality provided by Elastic Beanstalk. This requires additional security group and connection string configuration, but it also lets you connect to the database from multiple environments in addition to other more advanced features.