Hi Geoff,
Jessie and children arrived in Sydney 5 Oct 1912 - wow, according to newspapers, 1,164 immigrants onboard!!
http://trove.nla.gov.au/ndp/del/article/5341164?searchTerm=pakeha ....and corresponding crew! I have been through the crew list twice, and cannot find any crew member with that surname or anything that might look like it. Crew lists from that time period have ages recorded, and I cannot find any possibilities for your Phil(l)ip 1911 - 1913. Was he a good swimmer?

(I know he wasn't a good driver! SMH Monday 20 August 1928)
I am of the opinion that it would have been very unusual for Jessie to arrive on her own with nobody to meet her, and normally you find that the husband came out first to establish himself and the family followed. The other problem that you have is that passenger lists for that period will often just say "Mr Cohen" with no identifying info. They do sometimes list an occupation.
I have found a Mr. P Cohen (definitely "Mr.") arriving in Sydney on the
Otranto on 23 Nov 1911. The entry which appears to correspond (Cohen, 1911, age unknown) on findmypast lists this person as a female - perhaps worth checking out anyway?
What is the word above 1910 on his naturalisation record?
Debra