Currently, the cheapest month to rent a car at Daegu Airport is February. The most expensive time to rent a car is June. The cheapest prices for each month are shown above, but prices will vary based on availability, how far out you book your rental car, and of course, car type.
The length of time you can book a rental for is subject to the inventory of the supplier. When renting a vehicle from Daegu Airport it should be possible to rent a car for a whole month if needed.