Yep, Wake Up in Sydney is a great place to break the ice. There's a great bar down stairs and Wake Up organises great events e.g They do a walking tour of the city and beaches on Thursdays which is free except for the cost of public transport.
A high percentage of people travel to Australia alone. There is NOTHING to worry about...NOTHING!!! We're an English speaking western country, you can't get much easier than that, especially if YOU'RE coming from an English speaking western country. I'll gaurantee you'll meet up with a few people in the same boat as you as soon as you arrive here.
Make sure you get out of the city. The city = 1% of Sydney. There is MUCH MUCH more than the icons. If you want an idea where we ( the locals ) go and hang out just send an email.