It's not the same as traveling anywhere because it's to a different country. Whenever you take an animal from one country to another there are certain requirements. You'll need to check the specific ones for Ecuador.
Every country has its own rules and regulations about animals entering and exiting. You will need to check with the policies of Ecuador to find out what vaccinations are required.
You will need standard vaccinations and a signed health certificate from your vet. Speak with your vet about feline heart worm preventative and a microchip - invaluable for travelling pets.