[SalesForce] JQuery validation in VF page does not work in IE9

Try adding in the event parameter and a call to preventDefault() to your event handler. There might be something going on with the clicking of the command button triggering the form submit while at the same time the action function JS function is also submitting that Firefox is handling differently. I don't think your intention is to have the command button perform its default action of submitting the form anyway. Adding the preventDefault code on the event will prevent it from doing so.

Change:

$j('input[id$="sbutton"]').click(function() {
    afsave();
    $j('input[id$="sbutton"]').toggleClass('btnDisabled', true).attr('disabled', 'disabled');
});

To have the function take an event parameter and then call preventDefault on it.

// add parameter for the event, e.
$j('input[id$="sbutton"]').click(function(e) {
    e.preventDefault(); // add this line
    afsave();
    $j('input[id$="sbutton"]').toggleClass('btnDisabled', true).attr('disabled', 'disabled');
});       

You need to set a return value of false on complete of the actionFunction

try:

<apex:actionFunction name="doSubmit" action="{!submit}" oncomplete="return false;" />