Multiple Vertex Array Objects: Proper way to display multiple primitives?

I'm having a hard time getting multiple vertex array objects to render multiple primitives. Nearly all the OpenGL tutorials I've found online show using only a single VAO, so I'm not sure what I might be doing wrong.

I'm using Qt-OpenGL and trying to render a square and a cube (on multiple VAOs).

Using the following code, I'm only getting one primitive displayed on the screen (whichever one is initialized second). I can see either primitive when I turn off initialization of the other one, but not at the same time.

Data Struct:

struct VBO : public QOpenGLBuffer {

};

struct VAO : public QOpenGLVertexArrayObject {
  VBO vbo[1];
};
enum { CIRCLE, RECT, NUM_VAOs };
enum { POS, NUM_VBOs };

VAO vao[NUM_VAOs];

Initialization:

static void init_objects() {
  for(int i = 0; i < NUM_VAOs; ++i) {
    vao[i].create();
  }

  vao[CIRCLE].bind();

  for(int i = 0; i < NUM_VBOs; ++i) {
    vao[CIRCLE].vbo[i].create();
    vao[CIRCLE].vbo[i].setUsagePattern( QOpenGLBuffer::StaticDraw );
  }

  vao[CIRCLE].vbo[POS].bind();

  vao[CIRCLE].vbo[POS].allocate(circle.getVertexData(), circle.getNumVertices()*3*sizeof(float));

  vao[CIRCLE].release();

  // repeat for RECTANGLE instead of CIRCLE

  vao[RECT].bind();

  for(int i = 0; i < NUM_VBOs; ++i) {
    vao[RECT].vbo[i].create();
    vao[RECT].vbo[i].setUsagePattern( QOpenGLBuffer::StaticDraw );
  }

  vao[RECT].vbo[POS].bind();

  vao[RECT].vbo[POS].allocate(circle.getVertexData(), circle.getNumVertices()*3*sizeof(float));

}

Rendering Code:

void game::paintGL() {
  glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
  vao[RECT].bind();
  vao[RECT].vbo[POS].bind();

  QMatrix4x4 id;
  Game.setMVP( id );

  Game.setColor( Colour(0.0, 1.0, 0.0) );

  glDrawElements(GL_TRIANGLES, rect.getSolidIndices().size()*sizeof(unsigned int),
    GL_UNSIGNED_INT, &(rect.getSolidIndices()[0]));

  glFinish();

  vao[RECT].release();

  // Now for circle:
  vao[CIRCLE].bind();
  vao[CIRCLE].vbo[POS].bind();

  Game.setMVP( id );

  Game.setColor( Colour(1.0, 0.0, 0.0) );

  glDrawElements(GL_TRIANGLES, circle.getSolidIndices().size()*sizeof(unsigned int),
    GL_UNSIGNED_INT, &(circle.getSolidIndices()[0]));
  glFlush();
}

I've tried reading the data from the buffers before rendering (they are distinct and what I would expect for each primitive), so I know the write occurred properly. I'm guessing now I might be binding the buffers wrong, or missing a step while rendering.