In ‘Dalek’ the last remaining member of the titular species realises that it is the last. Its most pressing concern is where it will now receive its orders. It actually asks the Doctor what is should do now.
The Doctor wastes this opportunity, his order to kill itself only ignored because it still has a strong desire to ensure that the Dalek race survives. Ultimately it does self-destruct, but only because its DNA was corrupted by its exposure to Rose.
Could this Dalek have been given a new start? If the Doctor had given its orders would it have obeyed? This might have meant that the Dalek could have become a new companion, predating the possibilities of the Clara Dalek.
The Dalek does indicate that its sole purpose is that of a soldier. It only functions to fulfil orders given to it. It requests orders from both the Doctor and Rose, suggesting that it doesn’t care that those instructions come from non-Daleks (as it understands that there are no other members of its race).
The Doctor says that the Dalek honestly believes that all other species should die and that if it were to escape it would kill every living creature. Yet as a good soldier the Dalek could ignore its own desires in order to carry out any instructions given to it.
It would realise that if it did go on a murderous rampage it would draw too much attention to itself, that eventually enough firepower would be directed against it to destroy it. It is smart enough to know that this is counter to its desire for the Dalek race to survive.
The only way to ensure survival is not to give in to its instincts. This isn’t enough though. It still needs to have purpose in its life. It is a tool created for a specific purpose. This would not be the first time that the Doctor had found use for a soldier.
Bringing the Dalek onboard would be risky but would be a big step for the Doctor. This would indicate that there is hope, if two bitter enemies, the last survivors of the Time War, could work together.
The Dalek could combine qualities of both K9 and Leela, A genius who struggles to curb its instincts to kill. The philosophical debates between the Doctor and the Dalek could have been fascinating.
Given the proper circumstances the Dalek and the Doctor could have common goals. The Dalek would oppose any hostile alien life forms as not only are they are a threat to its well-being it could not tolerate another species successfully conquering the universe when the Daleks had failed.
Friendly or peaceful races were no danger to the Dalek. Protecting such lower species benefits the Dalek in the long run. For all their hate the Daleks could still appreciate the benefits of slavery. The Doctor could show the Dalek that it doesn’t need to put people in chains to benefit from their labours.
If the Doctor felt that he couldn’t trust an armed Dalek he could remove its weapon or at least reduce its power setting. The Dalek might find this tolerable, especially as the Dalek stun beam has frequently been shown to be very effective.
It is doubtful that the Doctor would trust the Dalek, at least at first. He has had experience before of the Daleks playing nice to achieve their goals. It is also likely that the Dalek would only remain loyal until it found a way to bring back the Dalek race.
There are many parallels to the Klein storyline in the 7th Doctor audios (‘A Thousand Tiny Wings’, ‘Klein’ Story’, ‘Survival Of The Fittest’, ‘The Architects of History’).
In those stories the Doctor is accompanied by a Nazi from an alternative timeline. Her philosophy is abhorrent but she is a product of her environment and the Doctor feels responsible for her situation.
Those stories allow Klein to be portrayed as a person, with some merits alongside her dark qualities. While she believes some terrible things there are things that she find appalling and evil.
The alliance between the Doctor and Klein is fragile. On more than one occasion Klein betrays him, with far-reaching consequences but there are also incidences where the Doctor misleads her.
Their relationship provides a good model for how the Dalek and Doctor might act as travelling companions. There would always be the chance that a Dalek would take advantage of situations, possibly at the risk of the Doctor’s own mission.
Eventually other Daleks would be encountered but this might not necessarily be the end of the partnership. Indeed the other Daleks may believe that the Dalek has been corrupted due to his long exposure to the Doctor and Rose and target him for extermination.
Faced with this the Dalek may renounce his former race and may not consider them to be members of his pure race. If the timeline stays consistent then he’d reject the human-Daleks in ‘Bad Wolf/Parting of the Ways’ and the Cult of Skaro.
If the Doctor didn’t want the Dalek to travel with him there is still the option of putting him with UNIT. This would make an unusual addition to any UNIT campaign set in 2012 onwards. After years of fighting against aliens they’d know have a powerful weapon against any future invasions.
There is of course the morale debate whether the Dalek could ever be redeemed. Is it innately evil? It could also be argued that evil requires choice, something that the Dalek never had.
Now it could be the influence of others that allows its to develop and grow. The trick would be persuading it not to see this as a sickness but an opportunity for something great.
All these possibilities grow out of the events of ‘Dalek’ but there is no reason that a similar situation can’t happen to PCs in your campaign. The could meet a similarly stranded Dalek, looking for someone to give its life purpose.
Other species can also be repurposed into an ally of the PCs. Command Strax has shown how a Sontaran commander can help save the day and the comic strips introduced Kroton, the friendly Cyberman.
Such stories can be used to explore themes of redemption and hope that are so prevalent throughout Doctor Who (especially in the wake of the Time War).