There is a way to put a turbo 13b in an \"MX5\" legally, but it's not a simple route and technically i'd be a eunos roadster...
The engine rules are based on a calculation based on the cars body weight. For Australian delivered cars this means the body weight listed on the RTA's (in NSW or similar regulatory body in your state) system. This means that you can't say teh car is heavier now cause you've added lead, or a bigger diff or accesories. This is the ruling orx626 is talking about that prevents you doing it to your current car.
The solution.
Find a nice Eunos in Japan, import it and comply it in Australia. Now is the tricky bit, you need to probably be friendly with the importer to manage this...
On teh import documentation make sure the car is put down as having a weight that allows you to add the desired engine (in NSW 1050kg will let you go 20B turbo

). That weight will be listed as your car's weight with the RTA, you may need a weighbridge certificate to show it actually weights that, so stock up on bags of concrete.
The fact the car is an import means it doesn't ft into the standard weights that teh RTA use, so they use your import weight. WIth your new heavy MX5/eunos, you can go to an engineering signatiory, and the RTA and get your new turbo rotary powered MX5 approved.
Feel free to point out any flaws in my system, but I know there are at least 3 turbo 13b \"MX5's\" that have been done this way, one was in NSW, I cannot recall the location of the other 2, but I have a feeling one was a Qld based car rego'd in NSW.