Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Dallas/Fort Worth Airport to Davao City as you normally would.
Due to multiple factors, expect to potentially pay more when booking in July. For low rates, October can be a great choice for travel to Davao City. Flights to Davao City from Dallas/Fort Worth Airport in October are about $1,186 on average during October, but can be found for as low as $822.