Is this dialogue OK?
Pwrson A -Are you jealous of her?
Person B -What am I jealous of her?

Question

Is this dialogue OK?
Pwrson A   -Are you jealous of her?
Person B    -What am I jealous of her?

Answer

Not quite.

What person A says is fine. 
What person B says needs revision. Here are some options:

What would I be jealous of her for? 
Why would I be jealous of her? 
Me, jealous of her? What for? (why)

What am I jealous of her for? (this might be used if person A has insisted that B is jealous of "her").