I'm not sure if this will work but you could try adding:
<div><form enctype="multipa...id="progress"></div></div>
To the Markdown.Editor.js file exactly where the X is placed (replacing it, of course).
var imageDialogText = '<h3 style="margin-top:0">Enter the image URL.</h3>X';
Note that you won't be able to disable the image upload filter from the Q2A settings. You'll have to use the minified version of the plugin in order to do so. There are a few changes you could make to fix this but it means making even more changes that are not considered good practices.
Edit: And there are more changes in that minified file that are NOT in the source files!
// The input text box
input = doc.createElement("input");
input.type = "text";
input.name = "wmd-promptinputtext";//zzz
input.id = "wmd-promptinputtext";//zzz
input.value = defaultInputText;
And also:
// The cancel button
var cancelButton = doc.createElement("input");
cancelButton.type = "button";
cancelButton.name = "wmd-cancelbutton";//zzz
cancelButton.onclick = function () { return close(true); };
Add the lines with the //zzz comment. Note this is the quick and dirty solution in order to avoid writing the plugin from scratch.
Finally, make sure your qa-markdown-editor.php file looks like this:
$html .= '<script src="'.$this->pluginurl.'pagedown/Markdown.Converter.js"></script>' . "\n";
$html .= '<script src="'.$this->pluginurl.'pagedown/Markdown.Sanitizer.js"></script>' . "\n";
$html .= '<script src="'.$this->pluginurl.'pagedown/Markdown.Editor.js"></script>' . "\n";
//
// comment this script and uncomment the 3 above to use the non-minified code
//$js = file_get_contents($this->pluginurl.'pagedown/markdown.min.js');
//if (qa_opt('md_enable_image_upload')) {
// $js = str_replace("<!--REPLACEMENT_UPLOAD!>", '<div><form enctype="multipart/form-data" id="qa_imageupload_form" name="qa_imageupload_form" action="upload.php" method="POST"><input type="file" name="qa_imageupload_file" id="qa_imageupload_file"><input type="button" value="Upload" onclick="javascript:qa_imageupload();" name="qa_imageupload_submitbutton" id="qa_imageupload_submitbutton"></form><div id="progress"></div></div>', $js);
//
//}
//$html .= '<script type="text/javascript">'.$js.'</script>' . "\n";