Installing Library Header Files with QMake

The problem

Since most of my projects are platform independent I like to organise them like Unix libraries. Unix libraries typically have the following directory structure:

./        Makefile(s)
./src     Source files and private header files
./include Public header files (that are to be installed)
./lib     Library build directory

The header files of the library should be installed into their own subdirectory of the common include directory. The code that uses the library can include the headers this way:

#include <mylibrary/myheader.h>

Copying the header files can be achieved in Visual Studio by adding a custom build step. The custom build steps allow the developer to customize the build process. But what about QT?