While Qt3D has a transform for drawing billboards, it is not very useful if you are drawing thousands of particles. This is because the transform can only be applied to one object at the time, and using thousands of objects is never a good idea in neither OpenGL or Qt. This is simply because the overhead of each object is very large, both in terms of memory and performance.
The solution I found was to write my own custom class that inherits QQuickItem3D and is capable of drawing a list of 3D points as billboards by directly turning each sprite towards the camera at every draw call. This is not very efficient, but it works and is way faster than the options: Drawing spheres or creating one billboard per particle. The ideal option is of course to use geometry shaders, but they are not easily available in Qt3D yet. Most likely because its a new feature in OpenGL 3.2.
The class is available on GitHub and the resulting output is shown in this screenshot: