I'm in a similar situation - I have to live with my ex-partner in order to stay in Austraila. We're on our 5th 457 visa, at the moment he holds it, for the last 2 years I did. We're hoping his sponsoring company will sponsor for PR after 2 years (we've tried this before but each time it's fallen through after 2 years of waiting, hence the number of 457s).
I completely understand your wanting to stay in Perth rather than return to the UK and leave him behind. It's a big decision to separate the children from their father and life in Australia is wonderful for children.
That said, the question is how you can remain. It's very hard to get a 457 unless you are approached by a company. I've managed it by being head hunted before, DP has managed by being in-situ with an organisation when one of our visas is ending and then asking for sponsorship.
The spouse who is currently de-facto on the visa is in the strongest position - they can find work anywhere. The spouse who holds the visa can't now work without a new visa being issued.
You need to act quickly. I would start a campaign with the job agencies - if you were sponsored before then you have specialist skills. Make sure your LinkedIn profile is full of key words and sells you hard - I get 3-4 approaches for work each month from LinkedIn.
Update your CV and pepperdash the agencies with it via Seek. Expect a deafening silence, do not mention your visa status on it. You will probably be called back for a job that is not listed.
If you are approached by a company this way then you are far more likely to get a visa or an offer of PR.
If your DH is currently the spouse on the visa then he should be pulling out the stops to get a decent job - he is eligible for working anywhere. Once he gets his foot in the door then he can ask to be sponsored. Having said that your visa expiry date is very soon. The majority of companies don't check up on visas once you've started so I expect he would be able to continue working once it has expired - obviously illegally and I wouldn't recommend it.
If you can you need to work as a team in order to stay in Australia. Alternatively you may have to return to the UK and attempt to get sponsorship again from there - it can sometimes be easier.
It's too late to attempt to go the PR route individually now, the process takes a long time and by the time you've got all the paperwork together they'll probably have changed the rules again .