VIC Australian Law - Can I Sue for Loss of Sleep?

Have you contacted the Environment Protection Authority? They have guidelines on certain noise levels and may be able to assist.
Suing your neighbour is a bit more complicated and can become very expensive. In the Magistrates' Court legal costs can easily escalate to the tens of thousands.
One action you may have is for what is known as Nuisance. Basically a nuisance is something that causes unreasonable and substantial interference with your enjoyment of your land. In this case, by way of noise.
Another action that is similar has to do with the Public Health and Wellbeing Act. Under that Act, the council is obliged to investigate noise that is a nuisance. You will need to approach the Council with doctors reports detailing the health issues that are being caused. Under the Act the Council must investigate and take action if it determines that a nuisance is occurring.
The technical issue with something like this is that what some people consider too loud, others do not.