The qresults list does contain a vertical-pane% as the container for the widget:
pane% objects cannot be deleted from their parent container.  Note that "deleting" an object from a container (such as a frame%) does not actually destroy the object, it just sets its style to 'deleted and makes it hidden.  This operation is not valid for pane% and classes derived from pane% so they cannot be deleted from their parent container.  All other objects however can be deleted.
As a workaround, I would recommend adding an intermediate vertical-panel% object to the frame and add the qresults-list% to it.  You should than be able to delete the panel.  Following your example in your original post, this would be:
#lang racket
(require racket/gui)
(define frame (new frame% [label "My Frame"]))
(define my-panel (new vertical-panel% [parent frame]))
(define my-pane (new vertical-pane% [parent my-panel]))
(send frame show #t)
(for ([this-child (send frame get-children)])
(send frame delete-child this-child))
Finally, deleting child widgets one by one will trigger layout re-calculations which cause visible flickering.  I would recommend either wrapping the for loop with the delete-child inside a begin-container-sequence /end-container-sequence, or using change-children, like so:
(send frame change-children (lambda (previous-children) null))
Alex.