Is what doing grammatically correct?

"What" is not a complete sentence and therefore cannot be grammatically correct on its own. It's a pronoun that usually acts as the subject of a sentence.

For example, you could say:

* What is your name? (Here, "what" is the subject of the sentence)

* What are you doing? (Here, "what" is the object of the sentence)

To understand if a phrase with "what" is grammatically correct, you need to look at the whole sentence.