There is very rarely a Docker image for any specific app that can be imagined. It may indeed be quicker to write a Docker file to do this than to go searching for one
The spec is rather brief, so I’d say at a minimum you’d need a GitHub token with the right permission(s), and then the right set of API calls to create a remote repo and to push a local repo to the remote.
Do you envisage this application taking input from a web app, or would console be OK?