You essentially have 2 hosts:
1. The host you have Docker on;
2. and the Arch VM on which you do not have Docker.
It does not matter that one is a host for a VM and that the other one is a VM guest. They are 2 different systems.
Now, to answer your question:
To move the Docker containers to another host, you need to turn off those containers first, you cannot move them while they are online.
Then, you use
docker commit to commit and save changes to the container's image. Afterwards, you can just copy the container image over to your VM (via
scp or any other such means). When you have the container images in your VM, you can just use
docker run to start them. It's as simple as that.
However, note that you do need to install
docker on your VM in order to do that. As I mentioned, they're two different systems. Virtual machine or not - they do not share anything besides hardware resources.