To achieve this you have to simulate a callback on the function triggered with the click event. For this make a function for the callback and a function for the click event:

Callback

function callbackAlert(){
    alert("callback trigered");
}

Click function

function clickFunction(event, callback){
    event.preventDefault();
    $("#testFrame").html('<object id="idObject" width="640" height="480" data="http://www.microsoft.com">');         

    callback();        
}

The just call it inside the ready statement of jQuery. Check this fiddle for the results.

You could create a little helper function that will take care of this. I've tested using the JQuery event "load"

References:

• http://api.jquery.com/deferred.state/
• http://api.jquery.com/load-event/
• http://api.jquery.com/category/deferred-object/

HTML

<input id="reload" type="button" value="Refresh"/>
<div id="MyObject"></div>

JavaScript

$(function() {

    /**
     * Helper to for the object element.
     */
    var HtmlObjectLoader = function() {
      var _this = this;
      this._loaded = true;
      this._deferred;

      /**
       * Load the object and HTML data.
       * @returns {JQuery.Deferred} Returns the deferred object.
       */
      this.load = function() {

        // check to see if the content is loaded.
        if(this._loaded === false) {
          // display in the log that the request is still in progress and a new one isn't being resent.
          console.info('..request in progress...');
          return;
        }

        // update the local flag indicating the status
        this._loaded = false;

        this._initialize();

        // **NOTE** you might want to put logic and round this so the "load" event isn't being continually bound.
        var $htmlObject = $('<object id="idObject" width="640" height="480" data="http://www.microsoft.com">')
          .on('load', function() {
            _this._deferred.resolve();
          });

        $('#MyObject').html($htmlObject);

        return this._deferred.promise();
      };

      /**
       * Setup the deferred object that is used to keep track of the request state.
       */
      this._initialize = function() {
        if(!this._deferred) {
          this._deferred = $.Deferred();
          this._deferred.then(function(){
            _this._loaded = true;
          });
        }
      }
    };

    var htmlLoader = new HtmlObjectLoader();

    $('#reload').on('click', function(e){
      htmlLoader.load();
    });
  });

Try

$(document).ready(function() {
  $('#reload').on("click", function(e) {
    e.preventDefault();
    var obj = $("<object />", {
      "id":"idObject",
      "width":"320px",
      "height":"240px"
    }).prop("data", "url")
    .appendTo("#testFrame").trigger("_ready")
  });    

  $("#testFrame").on("_ready", function(e) { 
    console.log(e.target);
    alert("frame loaded"); // Show a message when the page is loaded
  });
});

See also

Detect when an iframe is loaded

difference between iframe, embed and object elements

$(document).ready(function() {
  $('#reload').on("click", function(e) {
    e.preventDefault();
    var obj = $("<object />", {
      "id":"idObject",
      "width":"320px",
      "height":"240px"
    }).prop("data", top.location.href)
    .appendTo("#testFrame").trigger("_ready")
  });


  $("#testFrame").on("_ready", function(e) { // Not a real function
    console.log(e.target.data);
    alert("frame loaded"); // Show a message when the page is loaded
  });
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div id="testFrame" style="width: 320px; height: 240px; border: solid; border-width: thick;"></div>

<input id="reload" type="button" value="Refresh" />