Compatibility summary
You will need a travel adapter in Cocos (Keeling) Islands; plug types used there differ from Thailand.
Plug comparison
Thailand plug types: A B C O
Cocos (Keeling) Islands plug types: I
There is no common plug type between Thailand (A B C O) and Cocos (Keeling) Islands (I). You need a travel adapter.
Voltage comparison
Thailand: 220V, 50Hz
Cocos (Keeling) Islands: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.