The value you get from the sheet is already a date object (complete with year, date, hours etc), no further action should be necessary.
When you say 'next date' I guess you meant 'next day' ? If so, simply add 24*60*60*1000 to the date in milliseconds and you'll get the next day ;-)
In code it becomes something like this :
function xxx(){
var sheet = SpreadsheetApp.getActiveSheet()
var lastDateRow = sheet.getLastRow();
var lastDate = sheet.getRange(lastDateRow,2).getValue();
Logger.log(lastDate)
var nextDay = new Date(lastDate.getTime()+24*60*60*1000);
Logger.log(nextDay)
}
Logger result on a test :
Tue Aug 21 15:00:00 PDT 2012
Wed Aug 22 15:00:00 PDT 2012