You are not going to get CC points by paying the bill directly. Some options:
1. I have heard of some people paying their tax bills via the accountant, where they pay the accountant via credit card and the accountant then pays the ATO.
2. Have a friend pay the bill for you via direct deposit and you pay an equivalent bill for them using your credit card, or purchase the same value in say Coles vouchers for them. But this requires a suitable friend or relative that trusts you to make good with your end of the bargain.
I suggest that unless its a significant value of points then its not worth the effort.