And the successful candidate, likely to come from the A-League, will have some encouraging things to build on based on Tuesday's performance.
Along with promising striker Leckie opening his international goal scoring account, youngster Jason Davidson also had an encouraging first start while 25-year-old defender Rhys Williams was one of Australia's best at right back.
Lucas Neill had a solid match amid calls for him to step down, though Australia's defence was only tested in patches.
Neill equalled Peter Wilson's record of 60 matches as Socceroos captain.
Caretaker coach Vidmar made three changes to the side that fell in Paris, with Davidson named alongside Neill in central defence and James Holland pushed into central midfield.
Kennedy and Vidosic also returned as big guns Tim Cahill and Robbie Kruse were left on the bench.
Having not scored a goal in more than three hours of football, Australia were looking for an early strike to relieve the pressure.
Kennedy provided it before most of the 3741 fans had found their seats when he finished off some great build-up.
Williams and Vidosic combined out wide, with the latter producing a lovely backheel and Mark Bresciano finding Kennedy with a pin-point cross.
But rather than put the foot down, the Socceroos were put under some heavy pressure throughout the first half.
Simeon Jackson hit the post for Canada while captain Dwayne De Rosario should have equalised when he failed to capitalise on a sharp counter attack.
The Socceroos had a goal disallowed with Bresciano correctly adjudged offside in the 23rd minute while Mitch Langerak denied Tosaint Ricketts with an excellent point-blank save in the 30th minute.
Australia began to control the game and continued their dominance after halftime, with Vidosic doubling the lead in the 52nd minute.
The Swiss-based midfielder cleverly glanced in a close-range header in after Williams knocked the ball into the box.
Matt McKay almost made it three with a spectacular scissor kick before Leckie made it 3-0 when he headed in from David Carney's cross in the 79th minute.
Young guns Olivier Bozanic and Jackson Irvine were handed debuts off the bench in the second half, while Mat Ryan was given 45 minutes in goal and had little to do.