Shortcut to install Applications?
The simplest way is to just use the ⌥⌘S shortcut to show the Finder sidebar (which has the Applications folder by default), and drag the app there. You can then use the same shortcut to hide it if you prefer.

If you wanted a unique shortcut for copying a file to the Applications folder, you could make a simple service using Automator:


Open Automator, and create a new workflow, as a Service.
Set the options to Service receives selected files or folders in Finder.
Add a Copy Finder Items action, and set the destination to the Applications folder.
Save the service, and give it an appropriate name.
Open Keyboard Preferences, select Services under Keyboard Shortcuts. Find the service you just created, and assign it a shortcut of your choice.


If you wanted to get fancy, you could expand the service to automatically eject the disk image afterwards, but I'll leave that as an exercise to the reader.