After the bombing of Pearl Harbor from Japan did the plan work to invade Dutch East Indies right after?

Yes big time. The Japanese took it in stages over a period of three months. Starting in Dec 1941 when expeditionary forces were put ashore in the northern Malay Peninsula and on Luzon in the Philippines, and ending with the invasion of Java in February 1942. The Allies last final stand was the Battle of the Java Sea, Feb 27 where two relatively evenly matched forces met nose to nose in the Java Sea north of Java. The Japanese superior tactics and the Long Lance Torpedo won out hands down.

Yes. The purpose of bombing Pearl Harbor was to prevent the US from interfering with a number of Japan's military operations in S.E. Asia

The Japanese Empire occupied the Dutch East Indies, now Indonesia, during World War II from March 1942 until after the end of the War in 1945. The period was one of the most critical in Indonesian history. Under German occupation, the Netherlands had little ability to defend its colony against the Japanese army, and less than three months after the first attacks on Borneo, the Japanese navy and army overran Dutch and allied forces. Initially, most Indonesians joyfully welcomed the Japanese, as liberators from their Dutch colonial masters. The sentiment changed, as Indonesians were expected to endure more hardship for the war effort. In 1944–1945, Allied troops largely bypassed Indonesia and did not fight their way into the most populous parts such as Java and Sumatra. As such, most of Indonesia was still under Japanese occupation at the time of their surrender, in August 1945.

Yes, the Japanese won sea battles there and occupied the area.

The Japanese undertook to spread its empire and influence right across the pacific , attacking pearl harbour and numerous other British French Dutch colonies along with the Philippines which were American .

The US had to be completely removed from the way. You seem to have forgotten the strikes on Clark and Subic, too.

That being said, yes, the Japanese moved on the Dutch East Indies the day after bombing Pearl Harbor.

There was a delay of about a month in there while the Japanese took islands further north.

While the invasion was a "victory" for Japan it just did not work out as planned.

The allies were able to minimize the ability of Japan to have free access to the resources they sought. The allies still had air power to make things difficult and the US navy still had the submarine service to limit shipping of goods in and out.

No

Although the Dutch East Indies was one of Japans primary objectives the Philippines and Malaysia/Singapore needed to be effectively neutralized first.