You should do the month incrementing in the JavaScript and not in the PHP.
An AJAX request should return a value consistent with the parameters it has been passed. The way you want to implement it, it would also depend on an internal variable.
Your actual script also has little flexibility. It can only return the next month. What if you'd like to be able to return the previous month, or a specific month in the future?
In my opinion, you should change your AJAX script either to return the calendar for a specific month, or to return the calendar for the month following (or preceding) a specific month.