If I am travelling to US from Aus for example on Saturday morning, zuhr of Saturday will occur while on plane. Now when I land in US, it is still Saturday morning there and Zuhr of Saturday will occur a second time for me. Now please guide me which Zuhr to pray and which one to leave or pray both? What will be the niyyat in both cases?

When you have done Namaz Zuhr then the wajib has been done. It is mustahab to repeat it again if you reach when you arrive at your destination.