Does law school prestige matter?

I'm currently facing a dilemma and hoping for some advice. I am looking to start the JD next year, applying for UoM, USYD, Monash, UNSW and UWA - currently based in Perth. Chances of a CSP place look pretty limited (WAM of 76%, GPA 6.2, LSAT 162).

Wanting to work in corporate law, ideally for one of the larger firms. Only thing really driving me to go over east is the prestige associated with those universities. Other than that, my whole life is in Perth including a great paying (and flexible) job that I could continue whilst studying.

Is is worth biting the bullet and taking to risk to go over east? Does law school prestige really matter/will it influence employment opportunities?

Thank you!!!