Davout certainly knew on the afternoon of the 13th that the Prussians were heading in his direction. Why else would they attack Davout's outposts and Davout saw for himself and correctly deduced the reason.

Davout was in contact with Bernadotte in the early morning of the 14th and gave him Napoleon's order of 13 October with Berthier's note. That in itself ordered Bernadotte to march with Davout because they were basically co-located around Naumburg.

And I would suggest that Dupont, based on his own erratic behavior around Ulm, is not a reliable witness.

Sincerely,
K