The Korean Air pet policy is as follows:
Dogs, cats and birds to be carried in the cabin if they are older than 8 weeks of age and to be carried in the cargo compartment if they are older than 16 weeks of age.
Other animals such as rabbits, hamsters and snakes are not allowed in cabin or as checked baggage. Please enquire at a cargo agency for transportation.
Fierce dogs (as defined by the Korean Ministry for Food, Agriculture, Forestry and Fisheries), animals that are violent, on medication, ill, have a strong odor, or are pregnant will not be allowed on the aircraft. Brachycephalic (snub-nosed) breeds, which are susceptible to breathing difficulties or death during air flight due to their anatomical structure, cannot be carried in the cargo compartment. They may be carried in the cabin only if the carry-on conditions are met.
Taking a pet to a foreign country involves preparation and planning far in advance of your departure date. Requirements for pet travel to a foreign country are set by the destination country. If you are you traveling to another country and bringing along your pet you’ll need to meet the animal health requirements of the country you are visiting.
More information on Korean Air pet policy