I hit revered with BP before i hit revered with DO just by doing the daily quests. I'd say just do the quests, get a nice mount too.
You need to get the rep before you get the BG quest, so doing them now won't help you with that quest anyway.
JUST GO down by the blood elves in teh mines, drop your guild rep tab and grind out the final 3k. you'll get 25-28 rep per kill. that's only 40 mobs per thousand. they spawn so fast that it's like 1 hr. grinding and you'll get revered. maybe a little more but that's still short imo.