It’s an archaic form; the given sentence is not grammatical in modern English.
It’s an example of the passival, an archaic construction of certain passives (described well in this Language Log post). Apparently, at the time Austen was writing, “the trunks were being brought down” would only barely (if at all) have been considered grammatical; that construction (the progessive passive) first appeared in the late 18th century. The passival was the standard form, then, for what we would now express with a progressive passive.
As @RegDwight and @FumbleFingers point out, the passival is at least very close to the middle voice, the construction we use today in sentences like “dinner is cooking”, “the books are selling well”, and “you’re looking good!” Honestly, I don’t understand if there’s a clear distinction between the passival and the middle voice. Some sources I can find online (older ones) seem to regard them as the same thing, simply saying that this construction was acceptable in many more contexts in the past than it is today. Others (eg the linked LL post above) seem to suggest that historical linguists now regard them as two separate constructions. I’m afraid I am not au fait with modern historical linguistics; can anyone more knowledgeable clear this up?