Ok, so I have been playing around with QGIS console.py to see if you can do this yourself and it turns out to be pretty easier.
Open up console.py which, if you have installed using OSGeo4W, is in C:\OSGeo4W\apps\qgis\python\qgis. Then look for the python method called
def entered(self): and replace it with the following:
command = unicode(self.currentCommand())
if command == 'clear':
also add the following method after the entered method:
self.insertTaggedText("To access Quantum GIS environment from this console\n"
"use qgis.utils.iface object (instance of QgisInterface class).\n"
Save console.py and close, and restart QGIS.
clearConsole will clear out the console window and return it the way it was when you first open it when the
clear command is entered into the window.
However this doesn't clear the history, or restart any variables but I wouldn't want it to if I was using it.
Hope this helps with what you need.
EDIT: As of V1.7 this is a built in feature of the Python console. Just call
qgis.console.clearConsole() in the Python console to clear it.