You should be aware that this visa can take a really long time to get. Basically, they've said that if your job is not on the critical skills list (jobs that are highly required in the area you're moving), you should not expect to have your application finalized before 2012.
That being said, I do believe that engineers are listed on the critical skills list in some of the states. You'll want to looking into getting state sponsorship (even if by points, you don't technically require it) and getting it verified that your job IS on the critical skills list. Look into hiring an immigration attorney or reputable agent. If your career is on the critical skills list, they are supposed to be fast-tracking those applications. It could still take up to a year, all processes completed.
You'll need to get VERY familiar with the immigration
Australia website, and probably with the one for the state to which you want to move as well.
Good luck! It's a very involved process, that can take a LONG time. I eventually gave up on it after almost a year of trying to ensure my application would succeed and my job sponsored me to stay for another 2 years, but I was already in the country on a
working holiday visa which is not necessary an option for everyone (restricted to those under 30 years) and is definitely not a guaranteed route to getting sponsorship.
It may be possible to find a company willing to sponsor you to come to
Australia on a temporary (1-4 year) working visa, especially as an engineer (I have several friends here who are engineers from the
UK who are here on contracts with their companies) and from there, you would have better success at parlaying that into permanent residency.
Regarding your question about criminal record checks, you need a criminal record check from anywhere you lived more than 6 months (actually it might be one year and I'm mixing it up with Canadian immigration requirements but I would look more into that). Basically if you have only ever lived in Canada, you get your criminal record check through Canadian police services, and that's the only one you need. If you're already in
Australia you may need one from
Australia as well.