Welcome to the Bunnings Workshop community @bess. It's fantastic to have you join us and many thanks for your question.
What sized Hangi pit were you wanting to build? If you were thinking of a smaller variety, burying a Jumbuck Rustic Iron Fire Bowl would give you a great enclosure to hold the hot rocks and food. Alternatively, you should find this step-by-step guide helpful: How to build a fire pit. In your case, instead of building it above ground, you would build it below.
If you were to build the Hangi similar to the one pictured below, you could then make up a couple of decking board panels that covered it up once you're finished. I really like this design and feel it could be incorporated well into your garden plans.
Welcome to the Bunnings Workshop community. I trust Mitch's response was very helpful. Let us know if you need further assistance for this exciting project. We're looking forward to seeing how it progresses.