generally, if you make something up out of your head, you've designed something original. It has been known to happen that two completely unrelated people have come up with extremely similar designs, even close to the same time. In some ways, there is a limit to the variations or designs. (A hat is a hat is a hat, and all that) But creativity is limitless, and I think it would be fair to say that you designed at least part of that hat.
there are plenty of threads on here that discuss copyright, design, and so on, that may help you even more. As a rule of thumb, a stitch in and of itself cannot be copyrighted, though the particular way of writing it can be, particularly a complex stitch. Also a basic idea (ie purse, hat, etc) cannot be copywritten. How you apply the mechanics and stitches you've learned, and what you do with them, can be entirely unique to you, and therefore, your original design.
I hope that helps answer your question.