You'll probably find you're setting the date to Feb 31, 2009 (if today is Jan 31) and Javascript automagically rolls that into the early part of March.
Check the day of the month, I'd expect it to be 1, 2 or 3. If it's not the same as before you added a month, roll back by one day until the month changes again.
That way, the day "last day of Jan" becomes "last day of Feb".
EDIT:
Ronald, based on your comments to other answers, you might want to steer clear of edge-case behavior such as "what happens when I try to make Feb 30" or "what happens when I try to make 2009/13/07 (yyyy/mm/dd)" (that last one might still be a problem even for my solution, so you should test it).
Instead, I would explicitly code for the possibilities. Since you don't care about the day of the month (you just want the year and month to be correct for next month), something like this should suffice:
now = new Date();
if (now.getMonth() == 11) {
current = new Date(now.getYear() + 1, 0, 1);
} else {
current = new Date(now.getYear(), now.getMonth() + 1, 1);
}
That gives you Jan 1 the following year for any day in December and the first day of the following month for any other day. More code, I know, but I've long since grown tired of coding tricks for efficiency, preferring readability unless there's a clear requirement to do otherwise.