I think the doctor is able to care of whatever is the matter with your son.

不用替换。其实，whatever 和 what 都可以引导名词性从句。具体说，它们引导的都是名词性关系分句。区别是，前者具有强调意义：

whatever = anything that

what = the thing(s) that

句子有错误，即：care 是否为 cure 之误？请查原句是否还有错误。