Hi,
Mt Eliza is actually in Perth, its known as King's Park, and is right in the city. I believe there was an old men's home on the foot of the hill close to where a brewery was subsequently built (Swan Brewery). This reference has some information:
http://www.ntwa.com.au/alert/traces.pdf
This would certainly correlate with the place of death, at around that time.
http://www.bgpa.wa.gov.au/kings-park/history