Building Query String - Key Value Function

I have an issue building a query string. Basically, I have this:
/sites?order=site_numper_page=20&
But I would like to convert it to this:
/sites?order=site_num&per_page=20

I have tried this to check if the current iterator is less than the length of the object and if so, then add the "&", otherwise, don't. But it doesn't seem to work:
$.each(query_string, function(key,value){
params += key + '=' + value;
if((value + 1) != query_string.length){
params += "&";
}})