He had plans to cross on September 23, 1813 (see letter excerpted below).
A letter from General Harrison to Secretary of War Armstrong dated September 22, 1813, from Bass Island [in Lake Erie] indicated that:
"The greater part of the troops are here with me and the whole will I believe be up by twelve oclock. I shall proceed as far as the middle sister up the course of tonight & tomorrow& in the following night get or near the enemies coast as to land two or three miles below Malden by eight o'clock in the morning... ."
See a map of General Harrison's troop movements.