When travelling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Darwin is roughly greater than that of Balikpapan. You can assume this to be the case over the next 23 days.
You can imagine temperatures to be in the 34 °C range in October. The weather in Balikpapan is generally colder than Darwin's. As flight availability is subject to become more limited as peak season approaches it is ideal to book in a timely manner.