The time to take Darwin was immediately following their air attack on 19 February 1942.
Darwin was seen by both sides as an extension to the Dutch East Indies; it was included in the ABDACOM area and was the southern point on the Malay Barrier: the necessary line of defence of Australia and was recognised as such by the British, Australian and American High Commands prior to the war.
For the Japanese it was critical for the defence of their new possessions in South-East Asia. With Darwin and its surrounds in allied hands the D.E. Indies, Malaya and Borneo were all vulnerable to air and sea attack. The Japanese IOTL chose to neutralise this threat by ‘using a hammer to crack an egg’; employing the strike carriers that three months earlier attacked Pearl Harbour to launch an even larger air attack on Darwin and following it up with heavy bombers based in Ambon. They followed this up with repeated air raids for the next two years.
Just prior to the fall of Singapore in February 1942, General Yamashita submitted a proposal to invade and occupy Darwin and its surrounds, recognising that air attacks alone, no matter how successful, could not eliminate permanently the threat. This would have employed troops then on their way to Bali and Timor and the land and carrier based aircraft that were presently in the area, against which the allies had no more than a dozen P-40 Kittyhawks, a couple of B-17s and three heavy anti-aircraft guns. Landings in late February 1942 would have built on the disorder and confusion of the collapsing Allied command in Java. Yamashita’s plan called for a force of a division to be landed on the coast near Daly River Station and push inland towards Adelaide River and from there north – a total distance of two hundred kilometres, taking Darwin from the landward side. The coastal conditions were well known to the Japanese; in fact they had better maps of the north of Australia than the Australians had.
Once Darwin was in Japanese hands there would have been no possibility of conducting the air raids on South-East Asia that continually hindered Japanese efforts to get the Indonesian oil industry operational, or exports of other strategic resources from E.S. Asian ports that were obstructed by mines dropped by Australian and American B-17s. Nor would the commando raids that tied down so many Japanese troops in the region, 20,000 in Timor alone, have been possible. Japanese bombers operating from Darwin and Batchelor airfields could have hit any target in Queensland down as far as Brisbane, including the docks in Brisbane and Townsville where vitally important war supplies were being unloaded. In the west they could hit any target down to Exmouth, threatening to sever the air link to India. Such bombers could have operated unescorted and unhindered with no Australian modern fighter aircraft closer than Egypt, no more than twenty American P-40s transiting Australia on their way to Java, and only 17 heavy anti-aircraft guns in the entire country.
Once taken Darwin would have been secure: it could not be attacked from the south and an amphibious invasion would have to come from either the east or west. East would have to brave the narrows of the Torres Straits, where they’d have been sitting ducks to air attack from Darwin and Ambon and would have been well beyond the island hopping operations the allies conducted along the New Guinea coastline. An attack from the west would have been equally beyond the range of Allied air support without first building up a string of new bases along the west coast, or otherwise equally vulnerable to prolonged air attack before approaching Darwin.
Far from being at the end of a long supply line vulnerable to air and sea attack, Darwin would have been the anchor that secured Japan’s sea lanes in South East Asia from allied air attacks. It would have substantially changed the Pacific campaign in 1942 and ’43 if not longer.
Possession of Darwin would have made taking Moresby unnecessary, and would have made retaking Northern Papua New Guinea politically unfeasible while Darwin was still in Japanese hands; the A.I.F. divisions returning from North Africa would have instead been employed in an offensive to retake Darwin before any operations beyond Australia could be considered. The Australian A.I.F. and militia divisions represented the bulk of groud forces fighting the Japanese in the Pacific until 1944. (Excluding the Chinese)
As a small note, there would also have been no air evacuation of MacArthur from the Philippine Islands.