Very good question Susan, I hope someone who knows will answer, but please be very careful, stories of people moving in and once you fall out, they refuse to move out.  You could be opening Pandora's box.

I believe you need to declare and rent/board paid as income and that will reduce your pension. I believe that any income over $40 per fortight reduces the pension by $-50c for every dollar earned. Since you are on a pension however, it may well be that you choose not to charge rent if the tenant is able to care for you, do chores/repairs around the house etc. I dont know how Centrelink treats barter systems, but if no money is changing hands, it should not effect your benefit.

Toot2000 also makes a good point - make sure you have a couple of big, burley friends on hand if you need to give them the "heave ho".