I think I've figured out how to do it.

1) Create a ARGB8 Textute and QImage of the same size
2) Create a QPainter for the QImage
3) Render the scene into the image with QGraphicsScene::render()
3) Copy the contents of the QImage into the texture

My only thought is that because I'm using QGraphicsScene::render() I have to redraw the entire scene every frame, instead of only the stuff that changed.