For commit running container to image with new tag you can use this command :
$ docker commit <containerID> new_image_name:tag
For save new_image_name:tag to file use :
$ docker save -o new_file_name.tar new_image_name:tag
Now you can move your docker-compose.yml to same folder to another machine and your new_file_name.tar too.
On your mother machine where are this files run :
$ docker load --input new_file_name.tar
Rewrite in docker-compose.yml section image: to your new_image_name:tag
If you lost the name use :
$ docker images
and continue with $ docker load..... from above
Last step is run :
$ docker-compose up -d