This would do it for simple scenarios like the one you have:

var example = '05-10-1983';

var date = new Date();

var parts = example.split('-');

date.setFullYear(parts[2], parts[0]-1, parts[1]); // year, month (0-based), day

date.setTime(date.getTime() + 86400000);

alert(date);

Essentially, we create an empty Date object and set the year, month, and date with the setFullYear() function. We then grab the timestamp from that date using getTime() and add 1 day (86400000 milliseconds) to it and set it back to the date using the setTime() function.

If you need something more complicated than this, like support for different formats and stuff like that, you should take a look at the datejs library which does quite a bit of work for you.