Вот модель происходящего
<html>
<head>
<script type="text/javascript" src="jquery.min.js"></script>
<script type="text/javascript" >
$(function(){
$('#do').click(function(){
var df = document.createDocumentFragment();
var input1 = $('<input type="checkbox" id="checkbox1"></input>');
input1.click(function(){
console.log('click => ' + (this.checked ? 'true' : 'false'))
});
input1.change(function(){
console.log('change => ' + (this.checked ? 'true' : 'false'))
});
input1.click()
$('#result').append(input1);
});
});
</script>
</head>
<body>
<button id="do">CYCLE</button>
<div id="result"></div>
</body>
</html>