Hi Tom!
You should definitely remove the old version first. The best way to do this is to simply drag the Dropzone icon out of the dock. A dialog should then come up with an option to 'Uninstall Dropzone' - click this, Dropzone 0.6 will be uninstalled and moved to the trash. Empty the trash to complete the uninstall.
Then you can download and install Dropzone 2 from http://aptonic.com/dropzone/latest