No, you don’t necessarily have to practise rurally after graduating, and yes, you can still undertake specialist training after graduating. A lot of Australian universities have a rural program or rural focus of some sort, since rural practice is a big part of Australian health initiatives—programs are always changing and evolving to meet the country’s needs, and even Australian universities that aren’t ‘rural’ are quite likely to quiz you on rural topics during interviews.
For example, some students (mistakenly) believe that James Cook University (JCU) only accepts rural applicants since it has a rural focus. Although it’s true that JCU has a rural focus, you definitely don’t need to be a rural student to apply, and you don’t need to be a rural doctor after you graduate from their program either.