I don’t see quite this same option in 7.9 Community Edition. What version are you on? If it’s not 7.9.1, you should give strong consideration to upgrading versions at the same time you upgrade editions. Then it becomes a matter of downloading the correct version/edition bundle and following the upgrade guide. Once you’ve got your new instance up and running, log in and (assuming you’re a global admin) you’ll be prompted to go to the license page and enter your key. At that point, you’re good to go.
Notice I haven’t addressed “Docker” here. That’s because we currently only offer/support Docker for CE. We’re planning to get there with DE and EE, but I can’t give you any details yet. (Maybe for 8.0.) If you really want to do this via Docker then I believe you can edit your Docker file to point to the correct edition. (But I’m no Docker-ista.)
Back to your specific points
As I’ve noted above, the mechanics are slightly more complicated than what you describe, but basically yes. Drop your license key in to your upgraded instance and you’re good to go. Nothing to be updated / changed / reconfigured in your projects.