As with 'does' the 's' with verb infinitive is removed,so it should be 'want' at the end, but I am confused if 'what' changes the rule here and the sentence is correct...
You may be referring to the change from
She wants something.. to
She does want something.
When "does" is added to the expression, the plain form (infinitive) "want" is used along with it, because there can be only one conjugated verb in a clause. "Does" in that sentence is an auxiliary verb.
In your example sentence "She does what she wants.", there are two different clauses, "She does + complement", and the complement clause "what she wants". Since there are two different clauses, there are two different conjugated verbs, so the sentence is correct. "Does" in that sentence is not an auxiliary, but the main verb.