The original doom or doom 3? If you want a computer that can play games like Doom 3, Half-life 2, Battlefield 2, etc. you'll probably have to go over your budget. If you mean older games, something like the computer I have now would be fine (it played Diablo 2 really well, and even handles HL2 and BF2 on low setting decently).
Right now I have a 2.6 GHz Pentium 4, Sapphire Radeon 9600 Atlantis (like US$76 on newegg, so I'm sure you could find one for a good deal in Australia), and 512MB of RAM.