Qt has the moc/resource compiler that can do this for you. Not that you would/should shoehorn qmake into your project for it though, but they do it nonetheless.
Make you can use qmake as a prebuild step and include the generated moc files in your build? I wonder how many qt headers are in the generated source files.
qmake is not the only way to build Qt projects; CMake is quite straightforward and qbs works extremely well, too, though is rarely used in the wild (pity). I'm sure other build systems have sugar for Qt as well; CMake and qmake are just wildly popular.
Make you can use qmake as a prebuild step and include the generated moc files in your build? I wonder how many qt headers are in the generated source files.