New option `org-export-date-timestamp-format'.

* org-exp.el (org-export-date-timestamp-format): New option to
define the way a timestamp in #+DATE will be exported.
(org-infile-export-plist): Use the new option.

Thanks to Torsten Wagner for this idea.

doc/org.texi

@@ -9634,10 +9634,11 @@ Insert template with export options, see example below.
 @vindex user-full-name
 @vindex user-mail-address
 @vindex org-export-default-language
+@vindex org-export-date-timestamp-format
 @example
 #+TITLE:       the title to be shown (default is the buffer name)
 #+AUTHOR:      the author (default taken from @code{user-full-name})
-#+DATE:        a date, fixed, or a format string for @code{format-time-string}
+#+DATE:        a date, an Org timestamp@footnote{@code{org-export-date-timestamp-format} defines how this timestamp will be exported.}, or a format string for @code{format-time-string}
 #+EMAIL:       his/her email address (default from @code{user-mail-address})
 #+DESCRIPTION: the page description, e.g.@: for the XHTML meta tag
 #+KEYWORDS:    the page keywords, e.g.@: for the XHTML meta tag
@@ -9656,8 +9657,8 @@ Insert template with export options, see example below.
 @end example
 
 @noindent
-The OPTIONS line is a compact@footnote{If you want to configure many options
-this way, you can use several OPTIONS lines.} form to specify export
+The @code{#+OPTIONS} line is a compact@footnote{If you want to configure many options
+this way, you can use several @code{#+OPTIONS} lines.} form to specify export
 settings.  Here you can:
 @cindex headline levels
 @cindex section-numbers

lisp/org-exp.el

@@ -217,6 +217,11 @@ and in `org-clock-clocktable-language-setup'."
   :group 'org-export-general
   :type 'string)
 
+(defcustom org-export-date-timestamp-format "%Y-%m-%d"
+  "Time string format for Org timestamps in the #+DATE option."
+  :group 'org-export-general
+  :type 'string)
+
 (defvar org-export-page-description ""
   "The page description, for the XHTML meta tag.
 This is best set with the #+DESCRIPTION line in a file, it does not make
@@ -726,6 +731,7 @@ must accept the property list as an argument, and must return the (possibly
 modified) list.")
 
 ;; FIXME: should we fold case here?
+
 (defun org-infile-export-plist ()
   "Return the property list with file-local settings for export."
   (save-excursion
@@ -759,7 +765,15 @@ modified) list.")
 	   ((string-equal key "TITLE") (setq p (plist-put p :title val)))
 	   ((string-equal key "AUTHOR")(setq p (plist-put p :author val)))
 	   ((string-equal key "EMAIL") (setq p (plist-put p :email val)))
-	   ((string-equal key "DATE") (setq p (plist-put p :date val)))
+	   ((string-equal key "DATE")
+	    ;; If date is an Org timestamp, convert it to a time
+	    ;; string using `org-export-date-timestamp-format'
+	    (when (string-match org-ts-regexp3 val)
+	      (setq val (format-time-string
+			 org-export-date-timestamp-format
+			 (apply 'encode-time (org-parse-time-string
+					      (match-string 0 val))))))
+	    (setq p (plist-put p :date val)))
 	   ((string-equal key "KEYWORDS") (setq p (plist-put p :keywords val)))
 	   ((string-equal key "DESCRIPTION")
 	    (setq p (plist-put p :description val)))