cheap flight to Australia then East Timor from USA?

[rachelh]

I know one has to go through Darwin, Australia to get to East Timor. Any tips on how to get to Darwin, Australia on a budget? Then how do I get to Dili, East Timor from Darwin.

This also happens to be during busy months since I want to fly there in mid May and come back in mid August.

Any suggestions are welcome! Thank you!