Here are the avaialble non stops from DPS to Darwin:
Depart 330pm (that would be tight off the Timika flight which can see lots of weather delays) Air Asia 540 on Sun/Mon/Fri
4:15pm (probably doable) Air Asia 540 on Wed
and Jetstar 82 departs 6:30pm Sun/Mon/Fri as well. That's the safer bet ex Timika/Jayapura