I found it!
All I needed was QtWinExtras
http://qt.gitorious.org/qt/qtwinextras
My code now looks something like this:
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <qt_windows.h>
#include <QtWinExtras/QWinFunctions>
...
QPixmap pix(QSize(w,h));
...
HBITMAP hbm = QWinExtras::toHBITMAP(pix);
...
::DeleteObject(hbm);
I don't know if I need to include all those headers, but it works for me.