Your father should not lose any of his pension if he charges you board and lodging (even if he collects rent assistance). He would not be making any income from you, just getting you to pay for your own share of living expenses.
So as long as you say "board and lodging" and not rent, it should not affect his payment. You would receive additional from Centrelink in the form of "rent assistance" even though it is truly "board and lodging."
He can still earn a certain amount of income each fortnight without it affecting his pension anyway, and even that after the first one or two thousand (what they call working credits). My son pays me $340AU a fortnight for all his living expenses. This does not actually cover all the expenses, but I encourage him to save, which he does, and we also share chores. I pay all the rent, gas, electricity, water, NBN and food etc. so all he has to pay is for his own vehicle running costs and entertainment. So he is far better off than leaving home.