Different airlines and different companies. Both Australia and the US require local airlines to be majority owned (one of the reasons BA could not merge with Qantas). So one is a Ozzie airline and one is a US airline which cannot show they are part of some overseas global airline with different computer systems and ground handling teams
They could join separate airline alliances like OW or *Alliance or Skyteam but i think an airline alliance of airlines with Virgin in the name is a little too suspcious for airline regulators.