Comment by 3np
You can easily set up a Docker/CNCF registry[0] container running locally. It can be run either as a caching pull-through mirror for a public registry (allowing you to easily run public containers in an environment without internet access) or as a private registry for your own image (this use-case). So if you want both features, you currently need two instances. Securing it for public use is a bit less trivial but for local use it's literally a 'run' or two.
So you can do 'docker build -t localhost/whatever' and then 'docker run localhost/whatever'. Also worth checking out podman to more easily run everything rootless.
If all you need is to move images between hosts like you would files, you don't even need a registry (docker save/load).