I like it.

*grins* I love it! Thanks for making this for me, girl, I should make a Bones one for ya!

Uhura wanted the Enterprise not to be with Spock but because it was the flagship of the fleet iow the best ship to join hence her list of her qualifications. She did not say 'put me on the Enterprise so we could be together'.

"Farragut". Just for future reference in case you decide to continue this story.

... it's Farragut, not faragot... Also, ship names start with a capital letter, so enterprise should be Enterprise. Similarly, ranks used as a title: such as Lieutenant. Finally, blank lines separating lines of dialogue would make it easier to read. A bit more proof reading to check for spelling and punctuation will improve your readers' enjoyment.