The easiest way for TK to operate flights to SYD or AKL would be to append flights to an existing route. Something like IST-CGK-SYD and IST-BKK-AKL. There would be issues like getting permission to fly these routes (CGK-SYD and BKK-AKL) but these are the closest to the direct nonstop routes that you can get.

The longest flight segment on either of these would be around 5100nm so it could be done with any of their current long haul airframes.