There's an Add-on available that removes the header or footer in the active document only once added:
Documents by Top Contributors
Goto your Google Document and choose from the menu Add-ons > ...
Quora seems to create a random ID for the header each page refresh. Mine currently is ###__w2_aBrjao6_header. The consistent parts are __w2_ and _header, but __w2_ is used in other elements, sadly.
Google Search is not able to provide search results of that type, but there are other search engines which could pull this off like: