Karin, nothing to worry about here. It is just that MAV allows to book tickets only 60 days in advance, while for August 9 is out of reach yet. As of now last date for you can book is July 19. So just wait for a few weeks and you won't have any problems purchasing your 13 euro ticket
... could I just buy a ticket once I am in Budapest?
Sure, full fare one-way ticket is around 8000 HUF (app. 27 euro), but if you sure about date and connection, then it makes more sense just to wait until sale for August 9 is open and buy 13 euro ticket instead