No, you can start doing it anyway. The progress bar will move across as you meet the requirement. If you finish one and part of another when you return to port the progress bar will still be partially completed when you officially accept the mission later.
You could actually do both now and just rearm over and over and not return to dock until they are both done but I like to advance the date by docking after refitting once and spending all my torpedoes. I don't like finishing all my quests with 6-8 month to spare and then not have any missions until then. I know I can just go patrol wherever I want till then but without official orders I tend to fart around and not accomplish much.
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