You should be able to get the 100K bonus on just a 4 Continent OneWorld Explorer Ticket. Here is the info from the Qantas flyer, has some more of the rules and the fine print...
Visit the continents….
and earn 100,000 points

Qantas and the oneworld partners are giving you the chance to earn up to 100,000 bonus points.

Just fly with oneworld alliance partners to three or more of these continents:
- Europe and the Middle East;
- Africa including Algeria, Egypt, Morocco, Sudan and Tunisia;
- Asia including the Indian subcontinent;
- Australia and the South Pacific including New Zealand and Papua New Guinea;
- North America including Canada, the US, the Caribbean and Mexico; and
- Central and South America.
You must fly to at least three continents to start earning bonus points. For each flight you take, it’s the continent you arrive in that counts, not the continent you depart from. And each continent can only be counted once.

Fly to 3 continents – 5,000 bonus points

Fly to 4 continents – 15,000 bonus points

Fly to 5 continents – 50,000 bonus points

Fly to 6 continents – 100,000 bonus points

Offer valid for travel between 1 Jun and 31 August 2000.

(THE FINE PRINT)
You can only qualify once for this promotion. You must make a stopover to include a continent. A stopover is defined as an arrival at an intermediate point with a scheduled departure not within 24 hours. Bonus points will be credited to your Frequent Flyer account automatically on 30 November 2000. Any Account Service Fee that is due must be paid prior to travel in order to earn bonus points in this promotion. The maximum total bonus earned by any member is 100,000 points. Points are earned on all flights with a oneworld flight number, i.e. “AA”, “QF”, “EI” , “BA”, “LA”, “CX”, “AY”, or “IB” operated by a oneworld airline. For example, a flight with a “QF” designator operated by an “AA” aircraft will earn points. A flight with a “QF” designator operated by “XX” aircraft will not be eligible to earn points in this promotion.