In general your route is certainly feasible. Because you have to fly on the routes the member airlines operate, you'll find yourself taking unusual paths sometimes - for instance, Central America is regarded as part of North America for RTW purposes, so going from Quito to, say, Costa Rica may entail a flight from Quito to Miami, then Miami to San Jose, rather than a direct flight.

If you keep track of your alloted/used continental segments (6 in N. America, 4 in all others, not including intercontinental flights, 20 flights total) then you'll be fine.

Melbourne-Auckland-Santiago (S. America) - (Miami) - Central America - USA - San Francisco - Europe - Asia - Oz is fine.

And welcome to FT!