This year is a bit muddled up... should i put off starting my career?

Basically you need to prioritize your life. Make a list of what is most important to you. It seems that your trip and your surgery are taking priority in your life right now, so you probably shouldn't get the reputation of unreliability in the school system by starting something and then flaking out. I don't know how the job market is in NSW. It sucks here and teachers are lucky to get anything. Also I'm not sure when your school year begins and ends. It might be that you get your summer finished and then start the casual teaching when you can devote full time to it.