Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Dumaguete City to Kuwait as you normally would.
For a flight from Dumaguete City to Kuwait, you will be flying from Dumaguete. Dumaguete City (DGT) is just 3.0 km from the center of the city.
This is defined as Dumaguete City Airport (DGT) and Kuwait City Airport (KWI). Codes like Kuwait City Airport are often used to just call airports uniquely.