Yes download the qt-everywhere source tarball from "here":http://qt.nokia.com/downloads/linux-x11-cpp. Then extract it somewhere, configure it with something like:
@./configure -static -prefix $HOME/development/qt-static-4.7.2@
Then make and make install as per usual.
Once that is done, simply use the version of qmake that gets installed rather than the system-supplied qmake. You can do this by editing your $PATH environment variable to pick up your new qmake first or you could set up and alias or just use the full path to it.
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