@Mooloolabababy's advice is really sensible but unfortunately an employer can only sponsor you if you're on the skills shortage list.
OP the only way I can conceivably see this working (it sounds like madness, sorry) is if you live with Melb family, husband works 20 p/w as a brick layer WHILE studying. It is possible that by the end of his degree he'd then have the requisite work experience to get a skill shortage visa (which still wouldn't be permanent visa, but might be a pathway to one, assuming they don't take brick layer off the skill shortage list while he's graduating - they might and that puts you back at sq one).
Look into the rules on transitioning out of student visas.
Please also look up uni fees - they are not cheap. More than the UK, I believe. Aussies can take out loans as in the UK but as an international student on a temp visa who is expected to leave the country after graduation (in government's eyes) you would presumably need to fund it in full, every year, upfront. Do you have that kind of money? Say £20k minimum a year to sink into fees to get a qualification in an area that might be whipped off the skill shortage list by the time he graduates?
A much better plan is for you both to study and train in the UK in specialised, in demand fields where you know your skillset will be in demand - if not in Australia, then elsewhere. Canada, the EU, NZ.
Nursing, engineering, IT, trades, accountancy - do something solid and dependable that will enhance your warming potential even if the move to Australia falls through.