That's how most English speakers would probably say it, but technically "I am going home" indicates a present imperfect(unfinished/continuing) action that isn't explicit in the Indonesian. "I am going home" would be "saya sedang pulang". "I go home" is the most accurate English translation without changing the shade of meaning in Indonesian.
Even though defaulting to the imperfect aspect to describe most present actions is a common informal habit among native English speakers, using the simple present is another legitimate way to say the same thing, it just feels a little formal, like when JFK said, "We choose to go to the moon", or Thomas Jefferson wrote, "We hold these truths to be self evident", or Jesus' words were translated "I go to prepare a place for you". In Indonesian, the simple present doesn't have the same feeling if formality.
"I will go home" expresses present intent to go home in English. "Saya pulang" expresses simply the present, non-perfect action of going home, so "I go home" is the most accurate English translation, although "I'm going home" is probably how most English speakers would say the same thing.