Generally the most reasonably priced tickets with open dates (no fee for changing dates) are RTW fares. Otherwise you get into the expensive coach fare categories (Y, B, H fares), all the deep discount tickets have limited validity (30 days generally) and charge big bucks for change fees. Look into an LONE4 RTW fare on Qantas, that will let you route JFK-LAX-AKL-SYD-PER-SIN-AMM-LHR-JFK with up to 16 segments allowed (good for 12 months). Or use some student-only fares from STA Travel, but they tend to not be so flexible, and it sounds like your plans change often.