Create a new document library.
Create a new content type.
Add your newly created content type to the newly created list.
Create a new document.
Create your footer, or any other document template modifications. Then save document back to the SharePoint document library. Then close MS word.
Re-edit the MS word Document.
Add the Document ID Value to the footer. Then save the document as a word document template(.dotx) to the desktop or similar location.
Site Content Types > Content type >Advanced Settings.
Upload the document template just created.
Create new document to confirm your changes have been completed.
Make some changes to the document. Then save this document to SharePoint. Close MS word. Re-open the document, notice the Document ID value is now changed.
P.s. If you would like to use the Document ID as a label. The reference is {Document ID Value}