1. `bash-completion`をインストールする

bash

$ brew install bash-completion

2. `.bashrc`と`.bash_profile`に以下の内容を追加する

.bashrc

if [ -f `brew --prefix`/etc/bash_completion ]; then
    . `brew --prefix`/etc/bash_completion
fi

.bash_profile

if [ -f ~/.bashrc ]; then
    . ~/.bashrc
fi

3. Dockerのシンボリックリンクを追加する

bash

$ ln -s /Applications/Docker.app/Contents/Resources/etc/docker.bash-completion /usr/local/etc/bash_completion.d/docker
$ ln -s /Applications/Docker.app/Contents/Resources/etc/docker-machine.bash-completion /usr/local/etc/bash_completion.d/docker-machine
$ ln -s /Applications/Docker.app/Contents/Resources/etc/docker-compose.bash-completion /usr/local/etc/bash_completion.d/docker-compose

参考文献

Docker for Macをさくっと使うための入力補完