The process is a bit complicated, but you can book over the phone. If you call the Australian office number, you'll most likely be transferred to the call centre in Kuala Lumpur. There you will be able to request a particular redemption. IME they will then call you back within a few days to finalise the booking or, if the seat is not available, to offer an alternative. A bit time-consuming but I believe that's the only way to do a partner redemption. At least the lady I spoke to when doing this a few months back was nice and spoke English well.
I would probably have a particular flight/date that I know has award availability in mind before calling. That will make things much easier. If you plan to redeem points for an Emirates flight, you can check availability on QF.com. Or to search for SkyTeam availability, sign up for a Flying Blue account and search on the Air France website.
