$('#reportrange').daterangepicker({
    ...,
    function (start, end) {
        var dateRangeText = start.toString('MM/d/yy') + ' - ' + end.toString('MM/d/yy');
        vm.currDateRange(dateRangeText);
    }
});

self.currDateRange = ko.observable("09/24/12 - 09/24/12");
self.currDateRange.subscribe(function(newValue) {
   $.ajax({...});
});