Personally, I would hop on a plane. By the time you factor in the cost of hiring a car for 24 hours (premium rates apply for one-way hire); the cost of at least 4 food stops along the way (paying premium prices for very average food); and the cost of petrol for a vehicle large enough to carry 8 people... it would be cheaper to fly. You can get From Brisbane to Sydney for under $50 these days if you shop around, especially if you don't check-in any luggage but just pack a bag to take on-board with you.
To answer your other question, if you really want to do the car thing, then you really won't have that much time to be "doing things" along the way. Rest breaks of 30 minutes or so all add up. Besides, the highway now bypasses most of the interesting spots, so you would need to detour to do anything.
Just another point. Having driven from Sydney to Brisbane and return over 50 times in the last 10 years, I notice that there is much more police presence in NSW than there is in Queensland. So if you're not vigilent with your speed you can factor in the cost of a speeding ticket as well.
Take care if you drive, and don't use your mobile phone while you are driving.