Centrelink should have already asked you to update your income estimate prior to the start of the new financial year - usually they add $2K (or thereabouts) to your previous estimate and ask you to update if this is incorrect. Do you have an online account you can log in and check what your estimate is down as? Otherwise give them a call. They won't change the estimate based on the figure from your tax return.

I think if you are NOT lodging a tax return, then you can advise them of this (pretty sure this can be done on the online services too).

Have you received a payment summary/group certificate from your previous employer? If you have, it will show if any tax was with-held. You will get back any tax you have paid, as the tax free threshold is $18K I think.