It is indeed sad that your colleague's child is so ill but I feel that she is in the best of hands. Obviously, it is a complicated illness to have to be transferred from one tertiary center (KKWCH) to NUH Paediatric dept. I am sure that the Doctors are trying their best round the clock to diagnose the cause of the fever.
Fever is a symptom of an underlying disease. They are usually due to infections, be it viral or bacteria. However, some childhood cancers can present as undiagnosed fevers. Doctors will perform blood tests to determine if it is a viral or bacterial infection by looking at the white blood counts and other blood parameters. They will also check the child's urine and sometimes even spinal fluid to determine if the cause is due to urinary tract infection or meningitis (infection of the brain coverings). By now I am sure the doctors will have performed all these test.
Tertiary centres are manned by many levels of doctors, some are junior but every patient will be looked after by a consultant. Please get your colleague to speak to the consultants as the junior doctors may not be in a position to explain everything adequately.
I hope and pray that she will recover soon and completely.