The destination decides this, not the airline. A carrier can be perfectly willing to take your dog as checked baggage and still be unable to land it that way.
DestinationHow the pet must travelWhere it landsThe catch
United KingdomManifest cargoAn approved route — usually HeathrowPets must be booked as manifest cargo on an approved airline. Cabin and checked baggage are not entry routes into Great Britain, whatever the carrier will sell you.
IndiaCabin, baggage or cargoDelhi, Mumbai, Chennai, Hyderabad, Bengaluru or KolkataSix airports and no others, so the pet’s flight and yours may have to differ. Etihad excludes several Indian cities from cabin carriage.
PhilippinesCabin, baggage or cargoAny airport with a veterinary quarantine deskThe import clearance has to be approved before departure, and the microchip is absolute.
United StatesBaggage or cargoATL, DFW, LAX, MIA, JFK, PHL, SEA or IAD — directDogs must land at an airport with a CDC-registered animal care facility, with a reservation already made, and the airport must match the import form. No domestic connection first.
CanadaCabin, baggage or cargoAny port of entryThe most flexible of the six for a personal pet. A dog travelling to a new owner is a commercial dog, and those are barred from the UAE.
AustraliaManifest cargo onlyMelbourne International, directNot the cabin, not checked baggage, not another Australian city, and no domestic transfer afterwards.
The full rule for each country — vaccinations, titre tests, quarantine and timings — is on the travel requirements guide.