Generally every class can solo something 1-2 levels above. A hunter can usually handle 2-3 mobs at a time, in bad cases...2 on the pet, and 1 frozen. In these cases, a heal on the pet or hunter would help. If you’re mostly planning to quest on normal level mobs, then you have even less to worry about.
So your choice of duoing class isn’t as vital as you may think.
However, to reduce downtime, a healer type would be useful. A paladin or shaman can melee pretty well against another 2-3 mobs. A priest can fear things long enough to take out some mobs, but may not last long. However, the priest’s shield is very useful for the pet, as well as Fortitude. A druid’s thorns helps in the overall effect of taking out mobs, and also can use bear or cat to help out as necessary. Rooting a mob is also helpful.
Melee types like rogue and warrior also do great damage so that not having a healer isn’t as bad as one might think. Bandages and food take care of healing back up. A hunter with BM spec/spirit bond also doesn’t need to heal up too often.
I agree with the others about warlocks and hunters. Having a 4-some really can help out when fighting larger numbers, and both classes have pets designed to create aggro and keep it.