Hi,
Yes, you are right. The redirection will work only in case you would like to pass parameters to some other page.
Could you please descriebe why you need to pass query parameters to the page itself? Maybe there is an easier solution to achieve your goal.
If this functionality is necessary for your project, you could slightly
modify the menu web part you are using. Navigation web parts have
RenderedHtml property which you can modify before the page is rendered (so you could add appropriate query parametres).
More information about modifying RenderedHtml property you can find in this
thread.
Best regards,
Ivana Tomanickova