I went to Australia and the plan is similar to yours last year.
I suggest you not to go Melbourne, because the schedule is too tide, you may stay in Brisbane for 2 days and drive to gold coast afterward. We stay in a super nice apartment in Brisbane (Redcliff) for 2 day and really enjoy.
You no need to book the hotel from Gold Coast to Sydney, you may just stop in one of the motel in Pacific highway when you want to have a rest. We just stopped in around 1/5 distance to Sydney and then on the way to Hunter Valley before drive to Sydney.