Flying via Europe probably isn't the fastest way to get from Ottawa to Australia, but I've flown SIN-YOW a number of times, and YOW-LHR on AC + LHR-SIN on SQ is reasonably comfortable and probably the fastest possible connection between the two. (SIN-NYC-YOW might be faster in flight time, but transits thru the US and painful and there are no EWR-YOW flights.) LH is also starting YOW-FRA this summer, so that's another option worth considering, although long-haul in LH Y is pretty painful. Montreal is also easily accessible from Ottawa and tends to have more options and better fares.