Unable to re-define a function in my javascript object

I have an object defined using literal notation as follows (example code used). This is in an external script file.

if (RF == null) var RF = {};
RF.Example= {
    onDoSomething: function () { alert('Original Definition');} ,
    method1 : function(){ RF.Example.onDoSomething(); }
}

In my .aspx page I have the following ..

$(document).ready(function () {
        RF.Example.onDoSomething = function(){ alert('New Definition'); };
        RF.Example.method1();
    });

When the page loads the document.ready is called but the alert('Original Definition'); is only ever shown. Can someone point me in the right direction. I basically want to redefine the onDoSomething function. Thanks, Ben.

Edit

Thanks for the comments, I can see that is working. Would it matter that method1 is actually calling another method that takes the onDoSomething() function as a callback parameter? e.g.

method1 : function(){ 
           RF.Example2.callbackFunction(function() {RF.Example.onDoSomething();}); 
          }

Your code as quoted should work (and does: http://jsbin.com/uguva4), so something other than what's in your question is causing this behavior. For instance, if you're using any kind of JavaScript compiler (like Closure) or minifier or something, the names may be being changed, which case you're adding a new onDoSomething when the old one has been renamed. Alternately, perhaps the alert is being triggered by something else, not what you think is triggering it. Or something else may have grabbed a reference to the old onDoSomething (elsewhere in the external script, perhaps) and be using it directly, like this: http://jsbin.com/uguva4/2.

Thanks for the response .. in the end the answer was unrelated to the code posted. Cheers for verifying I wasn't going bonkers.