Short answer: No. Minimal-qml is a complete compositor, it doesn't need Weston.
Long Answer:
Wayland
is the protocol and IPC mechanism used by compositors and clients to talk to each other.
Weston
is the reference implementation of a compositor.
Qt Wayland
lets you develop your own compositor.
The binary produced by Qt Wayland can run wherever Qt applications can run, which means, you could actually run the compositor inside Weston, but It's not necessarily a good idea.
The most common use case is to run the Wayland compositor directly from a tty on the eglfs
backend. I.e. run the compositor like this:
./minimal-qml -platform eglfs
Then launch client applications inside the compositor by running
./yourclient -platform wayland