how do you figure that income you make doesn't affect your benefits?

Income is income as far as the tax department is concerned as far as I know.

Maybe what they mean is that you won't earn over $5200 (or whatever it is now) per annum which is the amount that you can earn before you pax any tax at all.

I would be ringing the tax office and centrelink and asking the questions so that you don't get stung later on.