You absolutely have a claim here. The area of law would be breach of contract on the grounds of promissory estoppel or potentially breach of the general protections of the Fair Work Act 2009.
You relied on your employer's promise of an employment position and quit your previous job to start work at your new job. You relied on the promise to your detriment, and suffered loss as a result.
Your entitlement to compensation is based on past economic loss, such as lost wages from the job you quit to the conclusion of the proceedings, and loss of opportunity at your old job, and also future economic loss, being the wages you likely would have earned and any potential for advancement in that new position.
Let me know if you would like me to help you with this.