Even though you have the Camps book, sometimes its good to get a fellow nomads view of a site. I'm amazed how different it turns out to be after advice from others on here.
Belanglo forest has some great free camp sites. check out the map or google it. a 4km drive in is a huge grassed area with toilets. There are other riverside spots further in.There is another forest on the sth bound side which has a largish aread to camp. (or just drive into forest near dusk and set up!) dont worry ivans locked up.
There are a couple of highway spots but can be noisy with trucks at night.I sometimes car camp at one of those as they closer to sydney, that way could get up early and drive through sydney at 4.00am and miss traffic and tolls.
Also if you drive nth from goulbourn on the old hwy, there is a huge area to camp about 4 kms nth of town.
As you drive between Goulburn and Canberra theres heaps of rest stops near Lake George. They are all pretty close to the Federal Highway so would be noisy . The best for an overnight stop is Edmonson VC rest area. We often stop for a cuppa there and its off the road far enough to bit a bit quieter. Its #701 in Camps 6