You can do this:
var someDate = new Date($('#textboxID').val());
someDate.setDate(someDate.getDate() + 1);
$('#someOtherTextboxID').val(someDate);
You could also extend the javascript
Date object like this
Date.prototype.addDays = function(days) {
this.setDate(this.getDate() + days);
return this;
};
and the call it like this:
var someDate = new Date($('#textboxID').val());
someDate.addDays(1);
$('#someOtherTextboxID').val(someDate);