BEFORE the bridge was built THAT side of the harbour was quite rural ... my forebears moved to Willoughby c1901 ... acres of farming and orchardists ... no running water etc ! They went from Newtown and Pyrmont to Willoughby because land was cheaper and the air was cleaner !
But 1909 Country directory ... cannot see any Kenna listed at all
Will check 1909 Alphabetical for Sydney ! back shortly
EDIT 1 1910 Alpha directory for Sydney ...

there's a doctor in the KENNA tree somewhere !
P R Kenna, ophthalmic surgeon, 193 Liverpool St (Sydney CBD) with pr (private residence) 6 Macleay St (in the posh part of East Sydney/Darlinghurst etc)
BUT none on the north shore !
P J Kenna was at Meredith St Homebush
George Kenna was at 212 Abercrombie St Redfern
I have only a few more directories to look up
JM