Interesting idea, but I'm not sure I follow completely. Philosophical zombies may have the same "thoughts", but they do not have qualia, they act like they do, but they don't. As for me, I'm pretty sure I have qualia. I've been watching this movie called "my life" ever since I was born. If I were to be a philosophical zombie, it all would have passed in the dark.

I think the phrase "I think, therefore I am" is the essence here. A philosophical zombie does not "think". It looks like they do, but it's just a deterministic result of neurochemichal events going on in a brain that lives in the dark. Something like a neural network for instance. They can exhibit thought-like behavior without experiencing anything(as far as we know).

If a zombie could detect it doesn't have thoughts, it would report about it. This can be done with reflection. If a zombie can't do reflection, that would be an observable functional difference from human, which is not allowed by definition. Therefore a zombie knows it has thoughts the same way a human knows it. A zombie only doesn't have qualia based on the assumption that it's possible to think without qualia.

If you have thoughts, you can't doubt whether or not you have thoughts. In order to do so you need to doubt yourself, which is a thought.

Did you answer to the right comment? I mean you can't prove you're not a zombie, thoughts don't help with this, because a zombie has all the same thoughts.

A zombie has no thoughts, that's the point.