You're not using the api correctly. Don't take it bad, it's confusing at first.
Both of these lines are telling the datepicker widget to initialize a datepicker on an element:
$("#datepicker").datepicker();
$('#datepicker').datepicker({
onSelect: function(dateText, inst) { alert("Working"); }
});
You could remove the first one since it's not doing anything except preventing the second one from having any effect.
If you want to change the value of one of the options after you've already initialized the widget then you would need to use this api:
$('#datepicker').datepicker('option', 'onSelect', function() { /* do stuff */ });
Or alternatively, you could attach a handler using jQuery's bind
function:
$('#datepicker').bind('onSelect', function() { /* do stuff */ });
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