Wouldn't burn it or give to the police. Give it to some poor people? I have a number of charities that I know could use the coin better than I would. My main concern would be how to monetise the btc without having to give 30% to the tax man.
I have no idea how charity tax works on Australia, but there are few organization which accept cryptocurrency without asking your identity. It's not endorsement/advertising, but Internet Archive is an example of such organization.
You could try creating ads about having found a paper wallet on social media and maybe some online communities that are popular in Victoria, Australia.
IMO it's beyond reasonable effort.