Compatibility summary
You will need a travel adapter in Christmas Island; plug types used there differ from India.
Plug comparison
India plug types: C D M
Christmas Island plug types: I
There is no common plug type between India (C D M) and Christmas Island (I). You need a travel adapter.
Voltage comparison
India: 230V, 50Hz
Christmas Island: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.