My home and contents is with NRMA and I have it listed as a portable item. I queried as to whether it has to be locked onto the car to be covered, they said no and that if someone removed it from the car with only straps it was covered. I'd say if it was in the back yard and someone came in and took it you would be covered.

Yes household insurance with designated items listed as portable like mbuzz says.

I have two boards insured on my Home/Contents and paid a little extra to have them itemised with their purchase prices. They were covered for their full purchase amounts when stolen off my car outside the house before going paddling one morning when I popped back in for a coffee. Thankfully they were located 8 days later. I can highly recommend AAMI for this, and I don't recommend insurers often! I'm located in Tassie.
Cheers and good luck.