Rule One: If the verb is modal*, then match the verb:
The verb used is to be (I am/I'm, You are/You're/, He is, etc.) because the verb in the first sentence is am though contracted to I'm.
The response therefore would use that verb too, but in the second person; you are or you're.
We tend not to end on contractions, so "Of course you're" would be strange, and so it's "Of course you are".
Rule Two: If the verb is not an modal, then you use do.
I found my car.
*Of course you found. [Incorrect]
Of course you did.
Rule Three: If the verb is not followed by an object or preposition, and ends the sentence, then you can choose between the two:
I don't dance.
Of course you dance.
Of course you don't.
*The modal verbs are be, can, could, dare, do, may, might, must, need, ought, shall, should, will and would.