Whether or not a car is necessary for your Corfu trip depends a lot on your Greece travel itinerary and your personal preferences. If you plan on basing yourself in Corfu old town for the entirety of your trip and just taking day trips out from there, you may just as well use public transport.
Do I need an international driving permit for Corfu?
Cosmos-Corfu Airport Car Rentals recommends you hold an International Drivers Permit except for your local driver's license. An IDL is written in 10 languages and serves as an officially recognized translation of your local driver's license in over 150 participating members of the United Nations.