Queens Park Rangers frontman Jamie Mackie had been in line to play as a lone striker against the Australians.
However, the attacker is suffering with a leg injury, which has led Levein to put his faith in Huddersfield's Rhodes.
"I had it in mind that Jamie Mackie would play but he has a calf strain, so Jordan will play," Levein told reporters. "You look at his goalscoring record, it's a tough one to beat."
Rhodes has made one senior appearance for Scotland.