Hi Emma : Your first problem is your Aperture. Anytime you go beyond f/11 or f/16 your lens loses quality. That's with any lens, but the cheaper lenses are even worse. By being in Aperture Priority, you
forced your Shutter Speed down to 6/10's of a second. That's pretty slow for being hand-held at 109mm. Here is a scale of f/stops.
http://www.cinemagraphica.com/tech/stop_scale.html
By enlarging your Aperture to it's largest amount available(f/5.6), you would gain 4 stops. That means your Shutter Speed would have adjust 4 stops to compensate for the difference in light availability.
Your speed - 1/60th of a second
1 stop - 1/120th of a second
2 stops - 1/250th of a second
3 stops - 1/500th of a second
4 stops - 1/1000th of a second
Now, that would take out any chance of camera shake.
Give it a try & I think you'll find that your "Kit Lens" isn't quite so bad after all.