My problem:
I have index.html:
In your case you can use $.post()
DOCS. If you gave your form an id="myForm"
then you could load the return data into the form's parent in the callback as follows:
$('#myForm').submit(function(e){
e.preventDefault();
$.post("toload.php", $("#myForm").serialize(), function(data) {
$(this).parent().html(data);
});
});