I looked at that too. Qt doesnt work natively on DirectX but it should be possible for the DX11 renderer with Angle, look at f.e. EGL_ANGLE_d3d_share_handle_client_buffer and EGL_ANGLE_surface_d3d_texture_2d_share_handle, needs a built of Qt with Angle for DirectX11. The native OpenGL backend might be even easier to bind to the UE4 OpenGL RHI, yet need another build of Qt. I didnt work on it yet, if you manage to get it done please PM me 
And as far as I know QtWebKit, well just the WebKit part, is LGPL even when you buy a commercial Qt version so platforms disallowing LGPL are out of reach.