CLOSE RANGE COMBAT
As mentioned at the start of this chapter, spacecraft fighting at ranges of less than 10km, or attacking vehicles or Travellers directly, use the normal six second combat round rather than the six minute round used for space combat.
Combat is conducted using the dogfighting rules for vehicles.
They don't fully, because they have additional modifiers and restrictions, as defined in the next sections. It's using a hybrid rules set, which you've interpreted in a sane and logical way (and the same way I would), but that's not the letter of what's written in the books. Example: If they are treating a ship as a vehicle in a dogfight, the text of the rules would allow vehicle skills to operate the ship. Personally, I wouldn't allow that.
Anyway once a dogfight is initiated, I can't find a rule that says it ends naturally after a round. You can re-initiatiate (to make a dice roll to get a bonus) but if you don't, what happens? In the absense of anything printed, does the dogfight continue? I think this is inherited from the core rules not defining when "combat" ends and leaving it to the referee to switch game modes as desired (for example if additional enemies are unengaged but a short distance away, the referee might handle the transition in the combat rounds, or they might not; and would this be one or two combats?).