Is there an app that allows you to take pictures when you push the volume keys?

You could try Camera Zoom FX?

That allows me to use my volume buttons (although it's pointless as my volume buttons are that fiddly, I never end up taking a pic of what I'm supposed to be aiming at). It might be phone dependant though.

 

You may want to try free Big Screen Button Lite (in the Market). It turns your whole screen into one big button.
And for a camera app I recommend you have a look at free Camera360.

The premier reason for 'terrible photo quality' from phone cameras is camera movement, resulting in blurriness of course. To combat this: support the camera. Let it rest on something solid if available. Or use your own arms for support: hold the phone camera with two hands and pull your elbows into your stomach for added steadiness. Don't forget to mind your breathing while shooting!