This is (indirectly) a duplicate of jQuery UI DatePicker - Change Date Format
To solve your specific example, change your input data-bind expression to
<input data-bind="datepicker: newDate, datepickerOptions: { dateFormat: 'yy-mm-dd' }" />
Your datepicker binding reads the datepickerOptions binding to supplies that object as options to the $.datepicker call.
var options = allBindingsAccessor().datepickerOptions || {};
Be careful when you upgrade to knockout 3.x as the allBindingAccessor has changed. More details from KO's doco -> Creating custom bindings