Is there a function to output the tag and vocabulary?
There is taxonomy_get_tree() which can return all terms in a hierarchical array, you will however still have to display it and hardcode the vid (or use variable_get() to make it overridable).

Depending on how and where you are displaying this, one of the following alternatives could maybe work better for you:


If you are displaying this information in a block, consider using http://drupal.org/project/taxonomy_menu instead. It can create menus based on vocabularies, which you can then be displayed as a block. They will be properly cached and faster than querying them on every page.
You can also use Views to build a list, tag cloud or similar thing for all terms of a vocabulary.