From Israel to New York is easy, also from there to South America, for example you have a 3 hour flight from New York to Miami and from there a 6 hour flight to La Paz-Bolivia, from La Paz you can travel to Peru, Argentina, Brazil and Chile and from Argentina you can take a flight to Sydney in Aerolineas Argentinas or from Santiago de Chile to Sydney in LAN Chile. As you see you dont have to return to New York and fly to Los Angeles to reach Australia, for less money you can go to Sydney.
Have a nice trip