Agree with many suggestions. Look at your words "kiwi" and "graphics" don't worry about where your website should go. your website should maybe not be in your logo? Not sure, people have different feelings about it. In any case, create the logo alone with no website, and then add it in later to places you will use it.
Kiwi is a great word. Think of things that you could do to imply Kiwi, but also "graphics" or a "design" idea. Sketch a lot
(I'm in college, still learning but these are the things that I've picked up on that are good to think about before starting a new logo)