What should I pass as --core parameter?
From the qd help output:


$ ./drush.phar help qd
Download, install, serve and login to Drupal with minimal configuration and dependencies.

Examples:
 drush qd                                  Download and install stable release of Drupal into a 
                                           timestamped directory, start server, and open the    
                                           site logged in as admin.                             
 drush qd --profile=minimal --cache        Fire up dev release of Drupal site with minimal      
 --core=drupal-8.0.x --yes                 install profile.                                     
 drush qd testsite devel                   Fire up stable release (using the cache) of Drupal   
 --server=:8081/admin --browser=firefox    site called "testsite", download and enable devel    
 --cache --yes                             module, start a server on port 8081 and open /admin  
                                           in firefox.                                          
 drush qd commercesite                     Download and install the "Commerce Kickstart"        
 --core=commerce_kickstart                 distribution/install profile, display watchdog       
 --profile=commerce_kickstart --cache      messages on the server console.                      
 --yes --watchdog                                                                               
 drush qd --makefile=mysite.make           Create and install a site from a makefile.


It should be inferred that drupal-&lt;Sematic Version Piece&gt; would be the project name you're downloading from the --core=drupal-8.0.x example provided.

So the following should work I believe:


drupal-7
drupal-7.x
drupal-7.N.x


Actually Drupal 7 doesnt follow semantic versioning. So D7 would require either drupal-7 or drupal-7.NN. The above drupal examples would apply to drupal 8 and beyond as of 06-01-2017 due to semvar usage in drupal.