Is there a keyboard shortcut to move the position of the Dock? Can I move the Dock using a keyboard shortcut? 

If there is no default keyboard shortcut, is it possible to set this up using a program?
There's no default, but you could probably use AppleScript to accomplish this.  Hmm...

EDIT:

Make an AppleScript to run this shell script: 

defaults write com.apple.Dock orientation -string left;killall Dock