The problem seems to be that you have "modules-inst" as the subfolder name, whereas it is only "modules" without the "-inst" suffix in reality.
See how it works fine on my end:
lpapp ~/Downloads/qt-everywhere-opensource-src-5.2.1/qtbase/src/plugins/sqldrivers/psql $ qmake psql.pro
lpapp ~/Downloads/qt-everywhere-opensource-src-5.2.1/qtbase/src/plugins/sqldrivers/psql $