I agree with NNW's listing of the most spectacular parts of the AAWT. Kiandra through to Rumpff Saddle/Mt Skene on the Jamieson/Licola Rd would cover nearly all of these in about 400 km.
In rural areas of NSW, you can catch a lift on the school bus, so Kiandra is potentially accessible by public transport. The school year ends in mid-December, but with careful planning you might be able to catch a bus up there on the Cabramurra-Tumbarumba route.
http://www.countrytransport.131500.com.au/index.asp?InfoMode=TownServices&Town=Cabramurra&ServiceType=School You would want to check this out next year before relying on it.
In terms of resupply, Thredbo and Mt Hotham are located just 2-4 km off the trail, and are nicely placed at roughly 1/3 and 2/3 of the way along the trail. (220 km from the start and finish, and 220 km from each other). Falls Creek is also an option at 7km off the trail, but given it is pretty close to Mt Hotham anyway, it doesn't add much in terms of resupply strategy. The advantage of town resupply is that you can get some fresh food, which helps with a balanced diet. A dinner out, a cold beer, a soft bed and the opportunity to dry out your gear can also do wonders for morale. It also saves you from having to do a 1500-2000 km road trip placing caches. You can also mail yourself any speciality items you think may not be available at the grocery stores there.
The downside of town resupply is that at 220 km apart, you are probably having to carry 10-12 days worth of food, which can be pretty heavy. Placing caches just off 2WD accessible roads enables you to cut this to 5-6 days of food.
In terms of gear, you need to be prepared for a summer blizzard at any time of year at those altitudes, say about -2C/28F. Wearing all your layers is probably a better way of dealing with this rather than winter gear. More likely is wind driven rain on exposed ridges at 5C/40F, which can be more far more dangerous in terms of hypothermia. Heat is probably the bigger problem - be prepared to carry 4 L of water on warmer days. There are several areas of the AAWT that are fuel stove only, so you will need to be prepared for that. Several sections of the trail are severely overgrown - you won't need a machete, but gaiters should definitely be part of your kit (gaiters also provide some degree of snake protection).
Totally agree that Chapman's book is excellent in terms of planning, and especially water availability (he's pretty good with differentiating between "sometimes", "usually" and "reliable").