If you are using Go (which solves most of your dependency problems) and SQLite (which means you don't need to integrate with an external database via service discovery) why do you need Docker at all?
In a production environment one would probably deploy using something like Fargate, Kubernetes or Fly.io.
Docker swarm mode is pretty good and terribly easy to get up and running in no time.
I have a few small personal projects hosted on Herzner on a couple of Docker swarm mode deployments with 100% uptime in the past two years, and all it took to get that infra up and running is installing Docker on a bare Linux node.
The only downside I'm aware is that inter-node traffic speeds can be relatively low.