Hi,
Regardless of which route you take, Brisbane to Hay is a long drive. Be prepared for white-line fever! The advice in the other replies about water, petrol, not sleeping in lay-bys & truck stops etc is all very sound as is the caution about driving at night. From experience, I'd add that native beasties like to mess about at the roadside at dawn and dusk. At least you know that they're not on stay-awake pills which is more than you can assume about drivers.
If $$$$$ is an issue, believe me, flying is much cheaper, more efficient and less stressful. However, if you need or want to drive,I'd recommend that you take your time and enjoy frequent stops in the towns along the way. It helps with survival and you can learn so much about this huge country. Remember that a lot of country towns do not have 24-hour or even late hours of opening so plan to get your provisions in daytime hours.
Keep your lights on, be alert, and keep a special eye on your speed within 50kms either side of Hay. The traffic police there net a fortune from drivers and are absolutely ruthless in their interpretation of the law!