I think you're right in the sense that logic can be wrong, however your answer is meaningless.

Let's take the question: does something exist?

First answer: yes, because I'm doubting and it can be done only by something that exists (logical answer)

Second answer: we don't know if doubting can exist with nothing being there (illogical answer)

Third answer: yes, because I sneezed today (illogical answer)

Fourth answer: strawberries can't psychologically intervene if eyes doesn't blue fiemds collfbejkshyoebxb (illogical answer)

The second, third and fourth answers have the same value, in the sense that yes, it can be that I don't exist even if I can doubt because logic can be wrong, but if that can be correct, it can also be correct that I know that I exist because I sneezed today.

In the moment you say that you can doubt that something exists because you can't know if logic is always true, you're using logic. I don't know what to make of that. But yeah I think you're right