If you want to access the store data in later request, you would have to store it somewhere. Django provides several ways to archive this:
1) You can use sessions to store the query: Every visitor who visits your site will get an empty session object and you can store whatever you want inside this object, which acts like a dict. Drawback: A single visitor can't do multiple searches with pagination concurrently.
2) Use cookies: If you set a cookie which is stored on the client side, the browser will append the data of the cookie to each request where you can access it. Cookies are more server friendly, because you don't need a session manager for them on the server, but the data stored in cookies is visible (and editable) to the client. Drawback: same as before.
3) Use hidden fields: You can add a form with some hidden fields on your search-result page and store the query inside them. Then, the client will resend the query whenever you submit the form. Drawback: You must use a form with submit buttons for the pagination on your page (simple links wont work).
4) Create Links which contain the query: Instead of using POST, you can also use GET. For example, you could have a link like "/search/hello+world/?order=votes"
and "paginated links" like "/search/hello+world/2/?order-votes"
. Then the query can be easily retrieved from the URL. Drawback: The maximum amount of data you can send via GET is limited (But that shouldn't be a problem for a simple search).
5) Use a combination: You might want to store all the data in a session or a database and access them via a generated key which you can put in the URL. URLs might then look like "/search/029af239ccd23/2"
(for the 2nd page) and you can use the key to access a huge amount of data which you have stored before. This eliminates the drawback of solution 1 as well as that of solution 4. New drawback: much work :)
6) Use AJAX: With ajax you can store the data inside some js-variables on the client side, which can then passed to the other requests. And since ajax will only update your result list, the variables aren't getting lost.