My point of view.
In order for to understand the Singapore Strategy, we must look what is the strategy about. In
https://en.wikipedia.org/wiki/Singapore_strategy, we find many answer but since this is a What If question, I came to believe if Australia had the resources to build up its military strength like aircraft, tanks, and army well maybe Singapore could have been better protected. Also if the other dominions would have participated like New Zealand, Canada, and Hong Kong, than Singapore would have been better protected.
There are two points which I would discuss in order for Singapore to be a successful fortress.
1) The air force: If Australia would have had early aircraft like bombers and fighters, then it would have been a good advantage for Singapore. Australia should have started to look up for its protection from the air against Japan and not wait for UK to send help. Now where would the planes be? Easy looking up many fighters that weren’t tested right, I found a good fighter that could have been useful for that roll. The Gloster F.5/34 (
https://en.wikipedia.org/wiki/Gloster_F.5/34) was a good fighter that was similar to the Japanese Zero. Imagine if Singapore had 4 squadron of this fighter plus other fighters squadron from the UK or the Dominions, then a squadron of 8 to 10 fighters would have held the Japanese. I would say 16 fighters per squadron plus 16 more in reserves. That would be a total of 80 fighters of Gloster F.5/34. The name of this plane has been listed as Griffon, Gallant, Gauntlet, Guardian, Grendal, Gannet, Generic, and Gawain.
2) Tanks: I won’t say Australia would not be able to construct tanks by early 1939 but one country would have been able to do it. Canada had a couple of facilities to build the Valentine tanks (
https://en.wikipedia.org/wiki/Valentine_tank) by early 1940. The only thing was that to construct a tank, it took months to build. But if the government would have put a leader to get the tanks by early 1941, well by November I would say a very good brigade would have been station in Singapore.
Australian forces (with the Exclusion of 8th Division which was in Malaya with 2 of its Brigades and the other split up between Rabaul, Ambon, and Timor) were based/fighting in the Middle east and North Africa as were the New Zealand forces
Canada had 2 Divisions+ in the UK but Government policy forbid them from being used elsewhere - eventually 5 Divisions would be used in the Liberation of Europe
The Canadian Government did send C-Force a 2 Battalion Brigade to help the Garrison at Hong kong - meaning said Garrison was only outnumbered 10 to one instead of 15 to one
Hong Kong cannot be held and has little to no strategic importance to the wider war effort - the best thing to have done is to expand the Hong Kong Regiment and Hong Kong Artillery to be powerful enough to force the Japanese to take the place by force and to be able to hold it long enough to destroy vital facilities and spike guns etc
The rest of the Garrison plus C force (in all about 2 Brigades worth) and the Naval assets (3 light DDs, 6 MTBs and 2 Insect Class Gun Boats) - go to Malaya
As for tanks
The only real way that Australia could provide any sort of AFV I think is if the Valentine tank enters production in the UK earlier than it did (the design was presented to the war office as early as 10th Feb 1938 so an opportunity to stand up production in 'non AFV' producing firms such as railway companies to act as the template!) and then enters production in Canada earlier than it did and then for the design to be picked up by Australia, initially built in low numbers in mid 1941 - and therefore completely butterflying the failed Sentinel tank project and its somewhat Phallic bow machine gun
So C Force arrives in Malaya with a 3rd Battalion with tanks plus sends 150 or so to Australia for the 1st Australian Armoured Division to train with and this formation joins 8th Division in Malaya with Australia's own limited production able to drip feed replacements to the forces in Malaya giving the forces in the region 4 Tank Battalions to add to the 'equation'.
The other issue is aircraft - more fighters and more pilots
I cannot help thinking that there was a greater demand for fighters and pilots elsewhere not to mention any extra planes would likely end up being shipped to the Russians (and tanks for that matter) so all other things being equal extra planes and pilots had they been available are unlikely to have been used to reinforce Malaya
So again I have to fall back on a Political reason to reinforce Malaya and for we need the Australian and New Zealand government's ITTL demanding more action post the Japanese invasion of FIC and this results in the 2nd Australian Imperial Force and the 2nd New Zealand Division being withdrawn back to Malaya and Australia and forming the core of the Imperial defence in the region as well as being provided with more squadrons etc.
This likely results from 2 things
Several British Divisions in the UK are sent to the Middle east/North Africa to replace the Australian And New Zealand forces (and who knows maybe this pressure allows for a Canadian Division to serve 'overseas' at this time).
This provides the region with 4 Tier one Infantry divisions (3 Oz and 1 NZ) not all of it in Malaya - we might see a Brigade level force at the following strategic locations - Rabaul, Ambon, and Timor rather than the ad hoc weak forces OTL
In addition several wings of Spitfires are freed up from Fighter command to reinforce Malta and North Africa at the same time (instead of making fruitless 'stupidly named' fighter sweeps across France and losing 400 planes and most of the pilots in the process) - this frees up several Wings of Hurricanes and P40s for service elsewhere and some of this say 2 fighter wings 1 each of Hurricanes and P40s ends up in Malaya - marginally improving things on the air front in Malaya.
This would all force the IJA to send several more Divisions to attack both Malaya and the Philippines
We are almost certainly going to see Op Matador with feckin bells on likely at Division strength rush the Kra Isthmus and the Landing Zones and additional forces available at Kota Bharu likely defeating the landing attempt being made there