It abolished the right to appeal to the Privy Council last year, but there are a couple of cases that had started proceedings that still haven't reached the main appeal stage yet e.g. David Bain case. They will still be heard over at the Council when they are due.
I doubt the Commonwealth will survive the present Queen, but who knows, maybe by those time some will tout the old-fashioned Empire ties as counterbalance to American influence (i.e. use the monarchy and British Empire as an anti-American jest)?
I think we can count on Australia becoming a republic as soon as the present queen is gone. Amanda Vanstone has said that Australia should be planning for a republic now while the queen is still alive.