stellamaire, great find on locating her death.
ashenique, I didn't see any article for Catherine's death (or marriage), but I didn't do a thorough search:
http://cdnc.ucr.edu/cgi-bin/cdncA James R Phillips is on the 1860 San Francisco census. He was born in Massachusetts c1833. I cannot view additional details. I don't know if he was married.
Most likely no connection to your Conlon's as you stated they were accounted for in Australia, but in the event one son left Australia [note: I wouldn't think that Catherine would have left Australia on her own, but perhaps she was looking for work??):
1860 San Francisco Directory
Conlon, John P, laborer, bds Manhattan House
[Apparently, Manhattan House was on Front and Broadway Streets]
http://archive.org/stream/sanfranciscodire1860lang#page/98/mode/1up1860 San Francisco Census
J P Conlon, born Ireland, c1832
I don't see him in 1861, but there is this person:
John P Conlan, laborer, S.F. Gas Co, dwl 1107 Kearny
1870 San Francisco Census
John P Conlan and his family, including a daughter, Catherine, born 1870.
http://www.rootschat.com/links/0vde/ SF Directories:
http://www.rootschat.com/links/0gfg/ [Click on "IA" to see the images]