I really don't see the Allies holding on to Sumatra once Singapore is gone. It's no Rabaul in the Rough that can be quickly expanded in time to fight off a determined IJA assault
This gives the Allies an opportunity to win time though. The OTL invasion of Southern Sumatra (Operation L) was done with less than 4,000 men. Sending a division to Sumatra instead of Singapore secures the approaches to Singapore as the Japanese need to find and assemble a (much) larger invasion force. They might have to wait until Singapore has fallen and the forces in Malaya are ready for the next push. OTL this was not until 28th of February (Operation T). This was at the same moment as the invasion of Java. The Japanese were adament that the invasion would not be launched without securing both flanks so that will be delayed until Sumatra is secure. In case the invasion happens and it's succesful the port of Oosthaven is available to evacuate Allied forces to Java. All this frustrates the Japanese timetable for it's offensives, even discounting any possible effect of OTL's Fall of Singapore.
Singapore is where the useful stuff like oil tanks and floating docks are that you need to run a modern war.
True. And all that usefull stuff was useless because it fell. We have already established that without Sumatra it was doomed anyway. So why no priority on securing that
deus ex machina first?
What does Sumatra have in comparison?
Except that it's vital to Singapores survival? It was also the primary reason for the Japanese offensive in the first place! The Palembang oilfields were needed to fuel the Japanese war economy. Without the DEI oilfields (of which Palembang was the most important) the Japanese will eventually run out of oil and will not be able to run a modern war.
Will the Dutch even let the Allies set foot there before the Japanese DoW?
Because the UK refused to guarentee the territorial integrity of the Dutch East Indies the DEI in turn had to stay neutral so this was impossible. There is no reason why forces couldn't be send after the Dutch DoW on Japan though (Japan only declared war on the Netherlands more than a month later).