Use a TemplateVM to install Docker and all the necessary programs you need, then create a new AppVM based on that template. As for the missing files, my guess is that you’re using classic volumes that are located in /var/lib/docker that are not persistent. Have a look at docker bind mounts and mount them somewhere in /home/user/ so they are available or use bind-dirs as @fsflover said. Also, note that docker isn’t started/enabled by default on Fedora, run this command in the template to make sure it starts when the AppVM boots:
sudo systemctl enable docker