I don't think Roger Douglas could become PM with a POD on or after the 1984 election simply because once he was Finance Minister and embarked upon Rogernomics his reformist impulses would run far ahead of the party and he could not carry the support of the party room.
Now, if Douglas became leader in 1983 after Rowling, he would probably be PM in place of Lange. However, once he started to implement Rogernomics as PM and as leader try to go further than in OTL (implement GFMI, flat tax or Ruthanasia style IR or welfare reforms) then Labour would most likely split.
In OTL Labour had a traumatic reaction to Rogernomics. In opposition afterwards Labour almost lost its major party status to the break-away left-wing Alliance. With Douglas as leader this possibility would probably increase.
Of course would this split occur while Douglas is in office? How would Douglas react to losing a leadership ballot while in Government?
Would he try to hang on in office a la Billy Hughes or Joe Lyons did in Australia by taking their supporters and joining the conservatives in a coalition?
Would Douglas and his supporters join National outright? If so would NZ First arrive early? These are all interesting possibilities.
As an interesting segway to a previous Kiwi WI you posed. Douglas as PM may leave MMP in the bottom drawer. FPTP in fractured party systems provide fascinating dynamics.