Is it possible to configure a virtualhost in a docker container with Apache?

You are using Docker now. Virtual host configuration should be inside Docker - not on your local Windows machine.

Create a volume (https://docs.docker.com/storage/volumes/), map a local Apache virtual host file to the one inside the container and set DocumentRoot to eliminate /project/my_project from the URL.

You can then setup Windows’ hosts file and add a domain (my_project.dev) to point to localhost.