Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Harrisburg to South Dakota as you normally would.
Due to multiple factors, expect to potentially pay more when booking in October. For low rates, August can be a great choice for travel to South Dakota. Flights to South Dakota from Harrisburg in August are about $411 on average during August, but can be found for as low as $189.