You're pretty darn far away from Peru. Check out LAN airlines, who fly into Santiago from Sydney via Aukland. When you buy your ticket, you can book a South America Pass with them (http://www.lan.com/en_us/sitio_personas/... for a discount on your flights within South America. LAN is the biggest and best airline in South America, maybe not quite up to par with Qantas, but you won't be disappointed I think.
The thing about booking flights with LAN, they change their prices from day-to-day, and even hour-to-hour for the same exact flights. So get on their website frequently and check your Sydney-Santiago flight, get an idea for prices, and when things are as cheap as you've seen them, it's time to buy.
Your total budget sounds perfectly reasonable for a good time in South America, for about a month or so. If you go really budget, you can stretch things out for another month. December is not the best season to see Machu Picchu, as it's the rainy season, but you can still see it. The Nazca lines are good year-round. With your South American Pass on LAN, I'd recommend you go to Patagonia and see Torres Del Paine, and the Argentine side near Calafate, Parque Nacional Los Glaciares. Iguazu is amazing as well, and will be very hot in December, but worth the visit.
One more thing, bring your student i.d. because a lot of places (including Machu Picchu) give student discounts.