I like it. So far, so good. I hope you go someplace "interesting" with it.
One question on the story, or rather on the background of you universe: How long does a person stay as an Ensign before getting promoted? The last person I asked that of said he allows someone to remain at the same rank for a full twenty-year career. Personally, I go by modern US / NATO standards: automatic promotion at two years from Ensign to Lieutenant-junior grade, and again at the four year mark to full Lieutenant. The reason I ask is because you wrote: "Her previous assignments were mostly temporary assignments on outposts or star bases." That made me wonder how many assignments and how long each lasted. depending on how things work in your world, she might be coming due for a promotion soon.
These are things you need to think about. You don't need to explain it all in the story, but you do need to makes some notes to yourself about your world. Things like: How big is the ship? How many officers and enlisted does it have? In my story, there are about 100 crew on board (including a dozen officers and five chiefs), and I've begun a list naming each person. If you're planning any combat scenes, you need to define what the ship has for weapons.
A few comments about the writing style. Punctuation is not perfect (who's is?), but it's far better than most fan-fic I've read. Bonus points for that. ;-)
The mix of simple vs, compound / complex / compound-complex sentences is much like my own style, so I found it very readable. Funny story: I had one critic who didn't like my style and kept asking for more simple sentences and less complexity. I sent him a private copy that I edited to read pretty much equal to "See Spot. See Spot run."
However, comma, when writing dialog, the normal rule is to switch to a new paragraph for each speaker. Now, you can pretty much break any rule you want. I don't care. For the most part, it was not hard to follow who said what. There were a couple places where the reader might get lost.