What you want is probably under the Sounds settings. In iOS 5 they are under Settings > General > Sounds. In iOS 6 Sounds have their own top level settings icon.
Either way, the very first setting is Ringer and Alerts. This controls all the system sound levels. If the button, Change With Buttons, is on, then system sounds change with the general volume levels. If it is off then they are set to whatever the slider says, unless the
iPad is Muted, in which case there are no system sounds.
I've noticed the the key clicks seem softer on iOS 6 than they did on iOS 5. Or maybe I'm just imagining it. Either way, max is max, and I don't know of any way to increase their volume.