Please try with the below code snippet.
var cal = $("#calendar").data("kendoCalendar");
var first = $("tbody > tr:first > td:first > a", cal._table).data("value");
var last = $("tbody > tr:last > td:last > a", cal._table).data("value");
Note : As java-script giving the month index, so you have to add +1 in month to get the exact date.