If you wait just to go to Costco for your petrol you will run out. There are not many Costco stores. I was at the Costco in Auburn 3 - 4 days ago and unleaded was $1.48/L. In the outskirts of Sydney, Metro and Speedway are cheaper outlets but none of those are on the main road to Canberra unless you don't travel on the freeways. There is a petrol station / food stop at Pheasant's Nest between Sydney and Canberra, near Mittagong, and again petrol if you leave the road at Goulburn. There is also petrol in the outskirts of Canberra. I don't know the brands but you don't have much choice, you just get what there is. Goulburn is a bigger city; if you are really fussy about brands you could take a drive through the town and do your comparison shopping as there is more than one service station. Expect petrol to cost more in Canberra than Sydney. Also expect to have to look for petrol stations in the shops, which are off the main roads. Canberra was planned so that there are small congregations of shops in the suburbs (supermarkets, restaurants, petrol) but they are hidden. At Dickson shops there is petrol. The main roads do not have shops and I can only think of one petrol station on Northbourne Ave, in the very north of Canberra, leaving the city.
We used to go to Canberra a lot until we got dogs who get carsick, but I might have some tips for you about Canberra / Southern Highlands. If you are a bit adventurous you might drive home via Batemans Bay and the coast road, but if you want to save time stick to the Hume Highway.
EDIT: I just re-read what I wrote. Goulburn is not bigger than Canberra but I meant it is a city of a fair size. Canberra is very spread out and it will be harder to physically find the service stations, they are literally hidden!
Lavandula