As the answer by Dale M says, you do indeed need a written contract. The contract should specify what rights you are buying, and what you will pay for them, and when.
The contract should be clear, and understood by all parties, if possible.
In some jurisdictions a contract transferring a copyright must be in writing to be legal. In any case, a contract involving long-term rights and possibly significant sums of money surely ought to be in writing, for the protection of all parties and the avoidance of disputes over what was agreed to.
Are you to own the copyright, or get a license to use the work. If a license, will it be exclusive? Will it be world-wide, or limited to a particular geographic area? Will i8t be permanent, or for a limited term? Will you have the right to create modified versions of the art?
How much pay?
How much will be paid for these rights, and on what basis? Will it be a fixed fee, or an hourly charge, or on some sort of royalty basis, whether on a per copy basis, or a percentage of the receipts, or of the profits?
Will payments be made on signing the contract, o0n approval of the design, on delivery of the final work, or at soem other time? Or perhaps payment will be in stages as the work progresses?
When must the art be delivered? What happens if it is late?
Will you have the right to approve or reject the work? If so, at what stage? What happens if you reject it? Must the artist try again, or is the contract canceled? How much if anything do you owe for rejected work?
How to obtain the contract
You could hire a lawyer to erite such a contract. But this is a rather commo9n sort of transaction. There may well be template contracts available, or software that drafts a contract from template sections based on choices made by the user. I am pretty sure that such exist for the US market, but I don't know about the Australian market. Such model contracts are often thoroughly reviewed, and may be as good as or better than an individually drafted agreement would be. But that depends on the quality of the source. Nothing stops a careless person from marketing poorly drafted contract templates, but then nothing stops an incompetent or lazy lawyer from practicing, either -- not right away at least.
You will need to choose your lawyer or source carefully.