From 28 March, Jetstar's website shows that JQ59 will depart Darwin at 15:05 on Wednesdays and Thursdays, with JQ60 returning at 1:15 the following day. There is no sign of the 3rd weekly flight.
The new flights are considerable cheaper than the existing flights, although overall fares are higher than normal as this period coincides with School Holidays and Easter, with no sign of price competition with the Silkair flights which commence on 26 March. From 17 April Jetstar are offering flights Darwin to Singapore from $129 and $89.90 return. Baggage and meals are extra.
The new Jetstar flights appear to disappear in May so perhaps Jetstar are still loading the full complement of new flights into their system?