Your better off not using Qt at all in regards to a 3D Game Engine. I worked on it for years with developers from Irrlicht, Ogre3D, Horde3D, Gameplay3D, OSG, SFML2, .... and have even tried to assist commercial Game Engine developers (Leadwerks) . You will solve one problem with integration and expose ten other issues. The way Qt's abstraction and just in general its designed is bad for games or external 3d graphics engines.
Qt5 makes the problem even worse.
I won't go into it, because core Qt devs never listen and tempers just git heated. But if you want to know what the problems are do a google search.
Without a huge amount of effort re-factoring some of Qt's core components like Autodesk or The Foundry had to do to get things to work out its not going to happen.
Valve, Leadwerks, Gameplay, ... all just used Gtk.
If you have the skills you would be even better off using ...
Poco C++
Boost
Luajit and Luawrapper
SFML2
Bullet
And OpenGL 4.3 or better
http://ogldev.atspace.co.uk/index.html
Drawing a pixel
Triangle
Shaders
Uniform Variables
Translation Transformation
Rotation Transformation
Scaling Transformation
Interpolation
Indexed Draws
Concatenating Transformations
Perspective Projection
Camera Space
Camera Control 1
Camera Control 2
Basic Texture Mapping
Ambient Lighting
Diffuse Lighting
Specular Lighting
Point Lighting
Spot Lighting
Loading Models with Assimp
Shadow Mapping - Part 1
Shadow Mapping - Part 2
Skybox
Normal Mapping
Billboarding and Geometry Shaders
Particle System Using Transform Feedback
3D Picking
Basic Tessellation
PN Triangle Tessellation
Vertex Array Objects
Instance Rendering
GLFX - OpenGL Effects Library
Deferred Shading - Part 1
Deferred Shading - Part 2
Deferred Shading - Part 3
Skeletal Animation with Assimp
Silhouette Detection
Stencil Shadow Volume
Object Motion Blur
http://nopper.tv/norbert/opengl.html
Rendering a Triangle
Grey Filter
Perspective Rendering a Cube
Phong rendering of a sphere
Texturing a Cube
Normal Mapping
Enviroment/cube mapping
GPU Particles
Geometry Shaders
Reflection and Refraction
Shadow Mapping
Simple Tessellation
Terrain Rendering
Water Rendering
Model Loading and Rendering
Clipping Planes and two sided Rendering
Using Stencil Buffer and Clipping
Rendering to texture and planar reflection
Texture matrix, alpha blending and discarding
Compute Shaders
Shadow Volumes
Displacement Mapping
Erode effect using perlin noise
Model with groups and materials
Fur rendering
Projection shadow for directional lighting
Screen Space Ambient Occlusion (SSAO)
CPU ray tracing
GPU ray tracing using computer shader.
http://antongerdelan.net/opengl/index.html
Hello Triangle
Extended Initialisation
Shaders
Vertex Buffers
Matrices and Vectors
Virtual Camera
Quaternion Quick-Start
Ray-Based Picking
Phong Lighting
Texture Maps
Importing a Mesh
Multi-Texturing
Using Textures for Light Coefficients
Fragment Rejection
Alpha Blending for Transparency
Spotlights and Directional Lights
Distance Fog
Normal Mapping
Cube Maps: Sky Boxes and Enviroment Mapping
Geometry Shaders
Tessellation Shaders
Overlay Panels
Sprite Sheets and 2D Animation
Bitmap Fonts
Vertex Displacement Animation
Particle Systems
Hardware Skinning
Morph Target Animation
Switching Framebuffer
Image Processing with a Kernel
Colour-Based Picking
Deferred Shading
Texture Projection Shadows
http://www.opengl-tutorial.org/
Opening a window
The first triangle
Matrices
A Colored Cube
A Textured Cube
Keyboard and Mouse
Model loading
Basic shading
VBO Indexing
Transparency
2D text
OpenGL Extensions
Normal Mapping
Render To Texture
Lightmaps
Shadow mapping
Rotations
Billboards & Particles
Billboards - Particles / Instancing
Picking with an OpenGL hack
Picking with a physics library
Picking with custom Ray-OBB function