Captain Michael Hooper leads the expanded 35-man squad but experienced utility back Reece Hodge misses out.
Playmaker Kurtley Beale, back in the international picture after returning to Australia following a spell in France, is injured and also misses out.
The series begins in Perth on 2 July.
Winger Vunivala switched to Queensland Reds in 2019 following a successful league career with Melbourne Storm.
"We picked him because of his massive potential," Wallabies coach Dave Rennie said.