BikeSA provide 3 levels of full cover for personal injuries to yourself during riding as well as membership. But it will not cover your bike. If you paid the extra premium, you can get loss of Income insurance which will pay a % of your wages while you recover. I pay a household cover which covers all members of my household including the LOI insurance for about $75 a year. Cheap peace of mind if you ask me.
http://www.bikesa.asn.au/RiderInfo_Membership_Cyclecove I use
Velosure to cover my bike while in use or at home which covers me for death or disability for up to $10k, the bike itself, against any theft, crashes and accidental damage, lost in transit caused to/by 3rd parties, and also covers my bike while in a racing event or any other corporate events like Amy's Ride, TDU, Grand Slam, etc.
http://www.velosure.com.au/WhatsCovered.aspx You can cover your bike at home under contents insurance for up to 5k (thats what it is with mine), but that cover may not insure you for the bike while its in use off your property. (check your policy)
This is the reason why I got additional cover with
Velosure to make sure I am covered for my bike against most common instances of accidents. Cyclogold is another great institution which works in conjunction with BikeSA personal cover so there is a chance you could combine the cover together as a package.