archive posts after a certin period of time

I am using a query to list posts on a special page template, and it’s working great, but I’m hoping I do one more thing with it. I want to be able to tell it to not list those posts which have been active for more than 30 days. For instance, If I make a post on the first of the month, then on the 31st day of the month, that post will no longer be included in the listings.

Here is the query I’m using:

<?php
query_posts('cat=7&showposts=12&random=true');
  while (have_posts()) : the_post(); ?>

(btw, the random=true comes from a plugin that randomizes the listings)

I have a feeling this is impossible, but I wanted to ask before I gave up.