Create short link automatically with ShURLy
As per the current module functionalities it does not seem to have that feature. So I think you need to create custom module.

In your custom module you will require to use hook_node_insert (For Drupal 7) this hook to execute after each node is added. Then Shurly provides API to create short link, using those APIs you can create short link as an when required.

Hope this helps.. :)