G'day Macca,
This is a difficult one mate, you have a very different case to many infact te majority of migrants to Oz.
Firstly for you it is a massive step due to your illness, (people with Asperger's Syndrome, deficits in social interaction and unusual responses to the environment, similar to those in autism) So this would test you to the limit in a new and very different environment like Australia. Add this to the responsibility you would then have for your Mum. mate, you would have a lot of preasure on you.
But no one should ever stop another person trying to do something. My first advice would be to speak to a really good migration agent. In a case such as yours you will need all the help you can get and definetly profesional advice. My experience of agents is limited but I know and hear many people speak very highly about GO MATILDA.
http://www.gomatilda.com (This is not an advert just a help to Macca)Their boss Alan Collett is an excellent guy, and they operate in UK and Australia. I think your first 30 minutes or so with them maybe free of charge. They would tell you straight off what your chances are of migration.
I hope all works out for you and that you get plenty of advice. Also as I tell anyone, always try and visit a place before jumping into a full big time move. Australia is very, very different to the UK
All the best,
BOB