Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Minnesota to Des Moines as you normally would.
Due to multiple factors, expect to potentially pay more when booking in June. For low rates, July can be a great choice for travel to Des Moines. Flights to Des Moines from Minnesota in July are about $254 on average during July, but can be found for as low as $133.