Krafty I suspect Vic will end up like the rest of the states with trailer rules that cover everything.
No problem until KLUNK and plod or the insurance company decides that your trailer wasn't legal.
Not registered? In NSW now, the small stuff still has to be registered, but it now longer has to be inspected each year. All they were really checking was that your lights worked and you had tyres with legal tread. they really didn't give a stuff about anything else, especially the draw bars now bowing after I stuffed up welding on angle to patch massive rust on them.
There are rules on how you must design your home built (usually in a downloadable pdf) and the regs in many states even have require stuff like the safety chain(s) meet a specific Australian Standard, including being marked as such and there is another A.S. for the shackles.
This came up recently on a camper trailer list.
AFAIK, in NSW, the manufacturer has to affix a plate specifying load, tyres, etc and you need to stick to that. Otherwise, you would have to show that the changes you made meet the built your own trailer regulations.
It is just my 2c, that there should not be any problem of changing the tyres, but you would need to ensure that it still met design requirements. The major problem would be ensuring mud guard clearances for larger tyres..
Different wheels shouldn't affect braking. Normally, you would just need to adjust the link/hitch higher to ensure the trailer was level. Stuff like type of brake (non, over ride, safety) is covered under the regulations and AFAIK varies by gross mass of the trailer.