My 33-34 Rogue had the same problem this week. I had trouble finding things to do. I did some grinding on the 32-34 cats up on the hilltops in Hillsbrad (way north of Southshore, just south of the ice patch). The mobs closer to southshore (through most of Hillsbrad) are 22-26, so they are too low for you.
At 34 I went to Stranglethorn and did the mid-level tiger/panther/raptor quests. Now I’m 35 and still lost.
At 34 you can get the ONLY Alliance SM quest (kill the top 4 bosses) which rewards a 30-dps weapon. But the pre-req is Anton in Stormwind, Anton in Desolace, and killing 30 of the lvl 37-38 undead in Desolace (My 34 rogue and a 35 paladin did it).
I do the shimmering flats quests from levels 30-34. There are plenty of 30-35 mobs there, so there’s unlimited grinding too. It’s a good place to solo grind.
The dark iron quests are group ones for players in their high 20s. I’ve never tried to solo them, so I don’t know what level can solo them. You have to fight level 27-31 elites, in groups. Some are ranged, some melee. What level is that? I wouldn’t try as a Rogue, but a Warrior might.