I think that you should treat yourself to a holiday in Oz. (You'll have great fun, I assure you. Apart from getting over the jet lag, going to Oz is hardly any different to going to, say, France).
Tell yourself that's exactly what you're going to do: Take a holiday and see a fascinating part of the world.
Tell your aunt that's exactly what you're determined to do. i.e, you're going to Oz to enjoy yourself. Then point out that it would rather silly if, while you were there, you failed to visit her.
That way your aunt won't feel guilty that she's dragging you half way around the world. Instead she'll understand that you'd like to see her while enjoying the holiday of a lifetime.
Go! Go! Go!
You'll never regret it!
Chris