これを試して:
date = new Date(2012,9,20)
Sat Oct 20 2012 00:00:00 GMT-0300 (BRT)
new Date(date.getFullYear(), date.getMonth(), date.getDate()+1)
Sat Oct 20 2012 23:00:00 GMT-0300 (BRT)
(Chrome と Firebug でテスト済み)
しかし、これは機能します:
date = new Date(2012,10,20)
Sat Nov 20 2012 00:00:00 GMT-0300 (BRT)
new Date(date.getFullYear(), date.getMonth(), date.getDate()+1)
Sat Nov 21 2012 0:00:00 GMT-0300 (BRT)