You do not have to queue with the same people, but you can.
If you choose a specific (we'll say Gnomeregan) you will get put into the queue for that specific dungeon. Other players that queued up for "Random" can be selected into your queue even though you queued up specific. The only downside of doing the specific is not receiving the bonus bag and experience.
If you queue up for a random, you will eventually get the dungeon that is not complete on the current list of dungeons that are available at your level. This is the way I go since you get bonus loot and experience every time, however the choice is yours. :)
To tell which dungeons are your level, or can be selected in the random queue, open your dungeon finder UI and click specific dungeons. This will give the list of the possible dungeons you can encounter.
Not all level tiers have the following setup, some only have Red/Yellow dungeons:
Red - "Hard" dungeon. A little above your current level.
Yellow - "Medium" dungeon. Currently at the right level.
Green - "Easy" dungeon. A little below your current level.