Issues in Farming Items as a Healer/Tank

Hi! I'm a new Wow player (only 2 months of gameplay). I have 1 rogue lvl 80 (3.5k GS) and recently I created a Holy Paladin (2k GS). I hit level 80 and I'm struggling with doing quests as a healer (I literally have no damage). I can barely farm some gold by doing quests (from what ik dungeons are not really for gold farming whatsoever) therefore:
- I can't get enough gold to buy items from AH;
- and with the reputation the same story: you gain reputation faster through quests than through dungeons only.
Basically I see this situation like this: as long as you are anything but DPS, you will struggle with farming stuff till you can do Heroic Dungeons/Raids.
So I was wondering.. how am I supposed to farm new gear (in my early lvl 80) if the 2 main options are: reputation and AH? (for a low GS character) and not spend lots and lots of time?
Thanks for any help!

Specific dungeons: Choose higher level ones only. You'll get some gear for your holy spec. The more gear, the more your judgement, holy shock, exorcism, consecration, seal of vengeance/corruption deal damage. More damage means easier time to get friendly reputations via quests to unlock tabards. You only need to get reputation factions to friendly, so that you can buy their faction tabards. Equip tabard and go do dungeons for more reputation.

You can use your 5.3K rogue to get gold via either quests or farming as well.

Damn I really forgot to mention: the Rogue and the Holy Pala are on DIFFERENT realms. - my bad. (the rogue part was to spot the fact that I have a lil bit of exp with a DPS)
Thanks! I will just do specific dungeons for a while I guess.

There is one more option - dual specialization. For 1 k gold You can unlock second set of talents, that can be used and changed anywhere.

As a holy, I would spend this 1k for dual spec, take retri off-spec, buy even some green items from ah (or get em by quests and dungeons - care for ninja looting here).

Even with uncommon items paladin is doing quite well while questing/gold farming ;)