Welcome to AFF
Chrismno
As mentioned, Kris Flyer miles can be used on any *Alliance airline (plus some others that aren't relevant here as other partner redemptions are restricted to certain routes).
Firstly, where in Canada are you? This may affect routing options - eg if you live in the east (eg Halifax, Montreal, etc) then you may be able to travel via europe and asia whereas further west (eg Toronto, Calgary, etc) you may be required to travel via pacific ocean.
Secondly, what class of travel? First class and business awards will be harder to get than economy.
Thirdly, when are you wanting to travel? December/January will be a tough time to get awards.
Fourthly, how many are travelling? A single award seat will be much easier to get than 2 or more. If there are a few of you then may need to travel separately and meet up at the destination.
Now you can help get award by being flexible. The most obvious way if the dates are fairly fixed is to look at alternative routings. Check out
www.staralliance.com electronic timetable for options. Taking as an example assuming you are from Vancouver and going to Sydney, we have
YVR-ICN-SIN-SYD on Singapore (ICN is Seoul, SIN is Singapore)
YVR-ICN-SYD on Singapore and Asiana
YVR-HNL-SYD on Air Canada (HNL is Honolulu)
YVR-LAX-SYD on Air Canada and United (LAX is Los Angeles)
YVR-SFO-SYD on Air Canada and United (SFO is San Francisco)
YVR-LAX-(AKL)-SYD on Air Canada and Air NZ (AKL is Auckland)
YVR-SFO-(AKL)-SYD on Air Canada and Air NZ
YVR-HNL-AKL-SYD on Air Canada and Air NZ
YVR-ICN-BKK-SYD on Air Canada, Asiana and Thai (BKK is Bangkok)
etc
You could also consider getting an award that takes you most of the way but with a (hopefully cheap) paid ticket at either or both ends - eg fly into BNE (Brisbane) and get cheap fare BNE-SYD. If you do this make sure you allow plenty of time to connect, since they are separate tickets if the inbound flight is late then you wont be protected.