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We work with a company in Australia who handle a few of our clients and I may be able to help but I don't think many Australian providers offer anything around your budget. Costs of pretty much everything are higher compared to US hosts.
With your budget, I believe you can get a lower end server specs but not sure if the hosting provider still provide that server specs. Like, Core2Dual, Atom processor. Alternatively, get a VPS at the initiative stage and then only upgrade to dedicated server.