If you like going in with a big 2H in PvE you're going to find a lot of people questioning you. DW is generally considered best for PvE, since it provides more stable damage over time, and because it generally scales better with gear. However, if you do want to, paladins just got a buff in that they can get 30% threat reduction, a slam warrior is a very good source of 2H damage, and enhancement shamans are not anything to scoff at.
If you want to melee DPS and are willing to DW, you could try a DW Fury Warrior, an Enhancement Shaman with DW and DW spec, a rogue, or a feral druid (granted cat druids count as just one weapon...but it's so fast I'll include here).
You could also try a hunter for ranged DPS, a mage for massive nukes, a warlock for insane DoTs, a balance druid for some decent nukes and a nice buff to spellcasters, an elemental shaman, or a shadow priest (which will help heal and regen mana to a small extent) if you dont mind casting.
All in all, you have several options to DPS. Some classes have several trees which are capable of DPSing well. I'd personally recommend for you a 2H shaman.
As to the "pallys only heal" thing...pallys make insane tanks, too. DPS in groups isn't one of their strong points, however it is better than their crowd control =P