Normally, WordPress handles redirection automatically. In your WordPress Dashboard, go to Settings > General. Your preferred URL (in your case http://doubtfulnews.com) should be in the WordPress address (URL) and Site address (URL) fields. While checking into this for you, I see that you are using WP Super Cache, which may be related to the issue you are seeing. I would recommend disabling and then re-enabling that plugin to reset it. Additionally you may want to change your Permalinks to something else and save the new structure, then set them back to their current settings and save again. This can refresh your .htaccess page which controls the redirects of your website.
Please let us know if you have any additional questions or need further assistance.
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