Before I moved here to live I always dealt with Budget and they did give airline discount, sometimes the discount for a long hire , (say six weeks), is better than airline discount. Things to watch, it can be 20% dearer to pick the car up on arrival at the airport with some companies, don't know about Budget these days but may be best to go into town and collect it from the town office, worth checking.
Some companies still want to limit you to 100kms per day and then charge extra for anything over the allowance, allowance negotiable usually, depends on company. They are all on the internet, just don't forget to end the URL with .com.au