So, just to put these characters into a kind of archetypal roles (this is dramatic relationship unrelated to any Starfleet rank structure or position on the ship), I’ll posit some things. This is NOT by any means the only way to look at them, but one that has been used to some effect by story tellers, past and present.
These are my notes while I was trying to figure out where your doctor might fit. I’m including them in case anyone might find it interesting. Please don’t think I’m trying to pigeon hole them, just trying to figure out where you might go with their story.
Captain Iopaz: I see her as a wounded hero. Her past has scarred her and changed her in ways she can’t fix by herself. She sees the mission as something that will help her, but there is a portal she needs to get through first.
Commander Zaffar: Mentor and partial Sidekick to Iopaz. But will probably spend time trying to re-create her prior relationship with this timelines Iopaz as a surrogate. She has her own journey trying to save her children.
Lt. Diogo: Ally: He’s cool and collected, but I see him butting heads occasionally when the tactical situation as he sees it calls for more extreme/forceful measures than the regular Starfleeters will default to. “Captain, we should raise the shields!” “No, that could be seen as a hostile act.” Etc.
Ensign Mopek: Ally/Sometimes Mentor. He’s an anomaly that I’d have to know more about. Does he exhibit any Cardassian cultural/behavioral traits, or is he simply physically Cardassian? I can guess that he’d probably be realty sensitive to people judging books, or situations, by their covers, and want to examine things beneath the surface to find out what is really going on.
Lt. Charleston: Ally. Assuming that her species reproduces like earth crustaceans, and lay many many eggs and don’t pay much attention to them. I would give her species a slightly less tolerant attitude towards those who need help in some way. They respect individually strong and competent individuals, but don’t have much time for the weaker ones. BUT encountering Starfleet (away from Klingon influence, which matched that cultural trait) Charlie has found that other viewpoints have validity, and is on quite a journey of self discovery.
Lt. Auz: I see him as a possible Shapeshifter (not physical, storywise, not always on of the good guys.) where his internal conflict may actually occasionally be at direct odds with those of the mission.
Lt. Etannis: Sidekick/comic relief. With a deeper story of her coming demise.
Counselor T’Rell: Mentor. The wise one people go to when they need help and are ready for the hard answers that they might not like, but will help.
So, you could create a Doctor that contrasts as many of the other crew as possible, while being really dedicated to keeping them alive (and enemy casualties if possible.)
Many of the crew seem highly aware of their mortality. The Captain saw her own death. Zaffar has seen her children literally wiped from existence. Etannis is from a very short lived species. So to contrast this, perhaps the Doctor could be exceptionally long lived. How about an El-Aurian (Like Guinan from TNG). This would also allow the El-Aurian time flow sense, or their understanding of it brought into play for Zaffar and the Captain.
The doctor’s sense of being a healer to any who need it would almost inherently contrast both Diogo’s war experience/security mentality where Diogo has probably made more of the enemy die for their cause than the doctor agrees with?
If Lt. Charleston does indeed have a lassez-faire approach to who lives and dies, that would contrast with the doctor’s desire to heal those who need it.
The long lived Al-Aurian in a single body gives a decidedly different perspective than the series of Trill hosts for a symbiont. So there is contrast to Lt. Auz.
AND lest we forget Counselor T’Rell. Healer of minds versus healer of bodies, but, while not technically the Counselor, the Doctor with a long range El-Aurian perspective might be able to over IDIC the Romulan/Vulcan counselor by being able to empathize and validate emotions of the crew who come to him/her.
That’s just my first impression, with some ideas and food for thought. Hope it helps.
Even if you don’t go with the El-Aurian, I think finding a way to contrast somewhat the other crewmembers would create a Doctor with a place in the story, instead of a background character.
As far as how many doctors, depends on crew size and automation level.. But really, what you want for your story. You could have a doctor and some really competent nurses, or more than one doctor.