I have not been to Australia on my own. But I have been there on two occasions. The first one I stayed with friends of the family. The 2nd time was with a relative. It will not be hard to converse in Australia since they speak English. Considering you are from the US as well, you don't have to know a different language. However, depending who you meet, there might be a slight accent that you might not be used to.
If I could say what it's like, consider it like visiting another state in the US. Of course, they drive on the opposite side of the road that we do so make sure you are looking at the correct side before crossing any streets.
I would say plan out where you will stay, what places you will visit, and look in Google maps or some other website to see where these places are located. Review the public transportation such as buses and trains and how you would plan in taking which bus/train route. Make sure that you know the times the routes end so that you are prepared to have transportation if you stay out late.
When you have things planned out, the anxiety will not be so bad. Sort of familiarize what you plan to do. If you visit the tourist places, you will likely be amongst other tourists from around the world. There are many other people that do travel on your own.
I had travelled to Paris, France on my own one time. Since I don't speak French, it would be a lot harder to communicate with most people. But to my surprise, there were some people who did speak English to help me if I got lost or wanted to purchase things.
I haven't been to Brisbane but only to Sydney and Melbourne. To make it easier for yourself, you can set up a shuttle or some other transportation to pick you up from the airport and to your hotel.
If you are bringing a laptop, you can get wireless internet access by getting the USB stick and sim card any any of the Australian phone companies. I know upon exit of the Sydney airport, there was a Vodaphone stand where they would sell this. I am sure the airport in Brisbane would have a similar set up. If not Vodaphone but maybe another phone company. I would say this would be cheaper than what you would pay for hotel internet access. Unless of course the hotel you stay may offer free wi-fi access.