Docker images are pretty minimal, But you can install ping in your official ubuntu docker image via:
apt-get update
apt-get install iputils-ping
Chances are you dont need ping your image, and just want to use it for testing purposes. Above example will help you out.
But if you need ping to exist on your image, you can create a Dockerfile or commit the container you ran the above commands in to a new image.
Commit:
docker commit -m "Installed iputils-ping" --author "Your Name <[email protected]>" ContainerNameOrId yourrepository/imagename:tag
Dockerfile:
FROM ubuntu
RUN apt-get update && apt-get install -y iputils-ping
CMD bash
Please note there are best practices on creating docker images, Like clearing apt cache files after and etc.