I answered your question on job prospects here:
http://community.boredofstudies.org/585/engineering/332493/engineering-job-prospects.html
Now career paths in EE are quite broad. You can end up in many different types of environments as an EE, including laboratory, industrial (factory-like), urban, rural and office like environments.
At UNSW you can do professional elective streams in energy systems, microelectronics, control systems, photonics, telecommunications and signal processing. Basically this means you can end up in many different work environments depending on your fieldwork. If you want to know more about any of these areas of EE, do your research on them. Each one can lead into many different areas and I strongly recommend you doing research to find out what jobs this can lead to (and you can also try looking up the types of jobs on seek, indeed, etc). Also, I suggest you taking a booklet from School of EET at UNSW info day regarding the undergraduate programs. That will explain each professional elective stream quite well too.
Do note that doing one of those professional elective streams isn't the be all and end all. If you do energy systems as your elective stream, it does not mean that you can't work with an electronics company (say Texas Instruments for an extreme case). At the end of the day you graduate as an EE which means you can work in any of those fields. However, employers will be more inclined to take you if you did professional electives relevant to the role available as ultimately you will most likely do your thesis with relevance to your professional elective stream.
I strongly suggest you go to Info Day on the 6th and talk to an academic about EE and what job prospects you have when you finish.