You might do best with the phlebotomy, or ECG technician work. Even then I think you will have to either get your US qualifications recognised here, or obtain Australian ones.
Psychologists in Australia don't make a lot of money really. I say this as a psychologist of over 20 years standing. Psychologists do a 4 year undergrad uni degree, then a 2 year masters on top of that. The registration requirements are fairly strict too, depending on which state of Australia you want to live in.
You might well get some sort of job in the community welfare sector in the drug/alcohol counselling area. Depends rather on where in Australia you would want to be, and whether you are able to obtain a visa that allows you to work here or not. They are pretty strict about work visas, and I've known people from the US & Canada be deported because they came here on visitors / tourist visas then started working and overstayed their visa. Our immigration detention centres are very unpleasant places, so you would be well advised to sort out all the visa stuff first, and if possible get yourself a job before you get here.