What else could then initialize this queue since the field member holding the pointer to the queue is private?

If this is really needed (and this goes for other FreeRTOS.rs wrappers as well), I'd much prefer to have a constructor API that mimics those from Rust's stdlib:

pub unsafe fn from_raw(ptr: FreeRtosQueueHandle) -> Result<Self, FreeRtosError> {
  // .,..
}

Optionally, this method could also do a sanity check by calling a peek or count method on the queue.