The issue here is that the document post type isn't created by Types but by the "Document Library Pro" plugin. I suspect that the post type wasn't set to publicly queryable hence why it doesn't show up.
What you can try doing is to create a documents post type using the slug "dlp_document" which should allow Types to take control of the Post Type settings.
From there you can re-activate your Document Library Pro and try creating the content template again.