Hello Averil,
It depends which state he died in. NSW and Victoria are pretty consistent in giving these details (and many others), and also Qld and the ACT, but the Northern Territory and SA don't, and others started to do so only after 1900 or so.

Have you seen this book, free on Google, called Ancestral Roots and Descendants of Charles Robert Looney and Lavanchie ... By Richard Coleman Witters? In particular p.62-66 (Chap.3). An interesting description of Rachel!

books.google.com.au/books?id=cNHNOfL3ra4C&pg=PA66&lpg=PA66&dq=rachel+redhead+john+looney+australia&source=bl&ots=pSTtXpRjCu&sig=GOuVoa63mrWZJafGCY4DmkuuTU0&hl=en&ei=pzAuTv-OE5H2swOktt34Dw&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCcQ6AEwAg#v=onepage&q=rachel%20redhead%20john%20looney%20australia&f=false

I don't know where "Sea View" was where John died in 1872 (according to the author), but Rachel died in SA so no parents' details if that's where John also died.

Sue