Yes, what Valky said. Darkshore area, on the other continent (Kalimdor) will have a ton of quests for you. Next one down (South) from there (Ashenvale Forest) has quests starting at level 20 or so. By then, all the quests that you couldn't get, due to too low level, will have opened up back in Redridge. Even skipping most of the collection quests, you shouldn't even come close to running out of quests, although I find that a few of the simple collection quests are quicker to do that running somewhere else to kill stuff.

Another option for you is to make a few runs through the Deadmines. Unless you're well geared, you might not be able to clear it yet, but you can get a ton of experience in there. Just clear as far as you can, jump out and reset it, and do it again.