Best design pattern for Javascript
Well if you want to use the Object prototype here is how I would structure it: 

// uses Object.extend for the constructor https://gist.github.com/rlemon/5256375

function Query(options) {
  this.value; // I would store the value in the object itself. Otherwise you should use this as a utility object and not deal with prototype. 
  // other defaults
  Object.extend(this, options); // extend options to the object
}

Query.prototype = {
  constructor: Query,
  removeStopWords: function() { .. return this;},
  stemmer: function() { .. return this;},
  convertBoolean: function() { .. return this;} // returns itself for chaining
};

var q = new Query({ value: ' Foo Bar Hello World ' });
q.removeStopWords().stemmer().convertBoolean();
alert(q.value);


But this is how I would structure it based on how I am assuming you are using this. If the use cases changed or the requirements were not fully understood I would possibly write it a number of other ways.