Can the "drag to applications" of a mounted DMG volume be done in the terminal?
Use this command once the .dmg is open to copy the app:

 cp -R /Volumes/Docker/Docker.app /Applications


The user will get the usual pop-up security window when the app is first run:



You can further automate the process by ejecting the disk image:

 diskutil unmount /Volumes/Docker


Then opening the app to get the security warning:

 open /Applications/Docker.app