You did not write what kind of game you plan. If you want something with 3D you should learn OpenGL which you can use with SDL. AFAIK you can't render with Qt in a framebuffer. You simply have a special Qt Widget in which you can display your framebuffer.
Maybe you want something like http://libufo.sourceforge.net That should be easier to integrate, it even has a sample SDL application. Do you know the http://nehe.gamedev.net tutorials?
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