Though the Allies didn’t know it, Japan had no intention of invading Australia; they did plan on isolating it after the fall of New Guinea and the Solomon Islands though. Their entire strategy depended on the Allies seeking peace before that was necessary. However, in the longer term, they planned on invading India to create a puppet buffer state under Indian Nationalists and a shoe string operation to occupy Ceylon (Sri Lanka) which dominated the Indian Ocean. With the British, Indians, and Chinese on the run in Burma, Indian antiwar demonstrations and rioting, Gandhi’s recent rebuffs of British guarantees of postwar independence (“a postdated check from a failing bank”), the formation of the Indian National Army under the Japanese, and the Japanese hitherto total domination of the sea, this was much more in the realm of the possible than we assume in hindsight.
On 30 March 1942 Adm Nagumo’s Kido Butai launched Operation C to destroy the recently reinforced British Eastern Fleet located at Trincomalee on the east coast of Ceylon. Once that was accomplished, the Japanese were to establish a submarine base on the Vichy French (a Japanese ally) island of Madagascar to interdict supplies to India, Egypt, and the Middle East.
The British, having partially broken the Japanese naval codes, knew of Operation C beforehand and reinforced the British Eastern Fleet with every available ship. Unfortunately, the British ships were mostly obsolete. The Eastern Fleet’s commander, Adm James Sommerville, had five battleships, but four were un-modernized “R” Class ships from the First World War, and the last, the venerable HMS Warspite was modernized but still obsolete. His battleships, designed to fight the German Navy in the North Sea didn’t have the range to operate in the vast distances in the East, so a secret refueling base was established at the Addu atoll in the Indian Ocean. Sommerville also had two modern fleet carriers and an escort carrier, but the fighters and torpedo bombers were also obsolete; they might have been capable of dealing with German and Italian battleships, but they were no match for the carriers’ planes that bombed Pearl Harbor.
Armed with intelligence of the Japanese attack, Sommerville sortied to meet them. Unable to find the Japanese, Somerville dispatched the escort carrier back to Ceylon while he moved to cover his secret base on the Addu atoll which he now (incorrectly) assumed was the first Japanese target. It was probably for the best because it put his most effective ships well out of range when the Japanese did strike.

Nagumo ravaged the Eastern Indian Ocean and the Bay of Bengal. On Easter Sunday, 5 April, he raided Columbo on Ceylon and destroyed the RAF on the ground and sank the ships in the port. On the 6th, 7th and 8th, the Kido Butai struck targets on the east coast of India, and sank any Allied ship within range, 23 merchant ships. On 9 April, he struck Tricomalee and caught the escort carrier, the Hermes, trying to flee whom he promptly sunk along with her escorts. With still no contact with Sommerville’s main force, Nagumo thought it best to retire after a job well done, if not completely finished, just as he had after Pearl Harbor. 

Sommerville’s Eastern Fleet would be pulled back to Kenya, but their mere existence would prevent further Japanese naval activity in the Indian Ocean in 1942, especially after the upcoming events in the Central and South Pacific in May and June.