Seeing the sandbelt and the rest of (worthwhile) Australian golf does not require three weeks. Two weeks would do justice to the region, provided you're willing to play 36 a day, and are there for the golf, not extraneous sightseeing
(in no particular order)
Day 1: Royal Melbourne West, Royal Melbourne East
Day 2: Kingston Heath, Victoria
Day 3: Commonwealth, Yarra Yarra
Day 4: Metropolitan, Huntingdale
Day 5: Royal Melbourne West again, Woodlands
Day 6: Ranfurlie, Peninsula North
Day 7: National Moonah, Portsea
Day 8: (St Andrews Beach, Gunnamatta and West courses)
Day 9: fly to Sydney, New South Wales
Day 10: Newcastle (two hour drive), fly to Adelaide
Day 11: Royal Adelaide, fly to Melbourne, fly to NZ
Day 12: travel, Paraparaumu Beach
Day 13: travel, Cape Kidnappers
Day 14: Back to the free world
Obviously you'll be exhausted by the end, and those hoping for a slower pace would need to spend 2 1/2 weeks here.
Tom Huckaby - you're gaining the day you lost at the end of the trip, so how is the two-day travel time at the start a logistical killer?
I've found during my short time in life that there are two kinds of people - the people who stand up and do things, regardless of what stands in their way; and the people who look for excuses. Looks like most of you are in the latter category.