You should be able to solo farm moderately well even as holy spec. I was able to get my epic mount on northdale launch 5 days after 60 just by killing satyrs and picking herbs. Once Dire Maul launches you can put some points into Holy Nova and aoe farm the lashers in DM:East for some good cash as well.
There is a huge misconception that making gold is difficult for healers or tanks. You will have to make intelligent choices and you will need to be a bit creative, but you can easily make a lot of gold without spending your time mindlessly grinding mobs. Though given your name @Grindhouse , I may be speaking out of turn. I usually make gold with a few basic methods...
Selling convenience. Selling convenience is based on the idea that you are selling something, that can be easily obtained by another player but that is gated behind an inconvenient cost. The most obvious idea here would be to run/summon a level 1 toon to first aid book vendors and begin to purchase them and mail them to your bank alt. Selling convenience can also be as simple as placing a mage alt in a major city (if you are dual accounting) and selling food/water/ports. You can do all sorts of convenience sales like creating silver rods early on for enchanters or copper tubes for quests, etc etc etc. Some of these can be profitable and others are a waste of effort.
Drone farming. Drone farming or bot farming doesn't require actual botting. This is the act of creating a small trickle of profit for a large portion of time and will only be valuable to people using two accounts. An example of drone farming would be to buy thick leather for approx 1.1-1.2g per stack and then craft nightscape tunics and vendor them for ~1.8g. This will slowly net you a profit but the crafting time is unreal. This is why this method is best used on a secondary account and wont be optimal for players with a single account. This toon sits in a major city spamming "WTB THICK LEATHER - open trade or C.O.D for XG pieces!!!" and standing stationary while crafting infinite items. This same method can be adapted to ANY crafted item. I have used this method by buying cloth that was under-priced on the AH and then creating bandages and vendoring them for a profit.
Selling your time. Tanks time is the most valuable, but a healer can be a close second. Sell your healing services or sell a key service to UBRS, Mara or ZF(mallet). You sell your time by reserving items in instances (popular on private but a touchy subject for players who have not played on private). You could even lump herb farming or any gathering profession into this category. Your time = ~Xg per hour. Depending on what you have to leverage you will either be more or less valuable than other players. If you do decide to grind, farm items that are easy for you to kill, like https://www.wowhead.com/item=2091/magic-dust which is available on low level mobs in Westfall and will be highly desireable for PvPers (in vanilla this item works on players above 30 as well - tooltip is updated for retail).
Flipping items. Knowing the value of items can payoff huge. This has the highest potential value vs effort. People did not know the value of items in retail vanilla, many do not on private and I doubt many will in Classic. You can buy green item wands (of shadow wrath, of frozen wrath, dragons finger) or other items and if they are itemized correctly they can be a BiS piece forever. Yes. You can buy a green item on the AH for around 3-5g and sell it for upwards of 2000g if you can identify its value. This method takes a bit of capital but can pay off eventually. This works best if you have a second account to scan the AH on your secondary monitor while playing.
Selling cooldowns. Profession cooldowns like alchemy transmutes, tailoring mooncloth or leatherworking for cured leather hides. Having max professions 300/300 skill requires level 35. You level some toons to 35 and get them maxed out professions and then sell their cooldowns each day. Depending on the phase and your server competition these cooldowns sell for anywhere between 5-25g. You log in, you click the cooldown and you logout. This is especially valuable for players who are adept at powerleveling.
Investing in the future (requires capital). The final method and the safest method of investing is to invest into the future. You have the phases, you know the patch cycle and you have a crystal ball, use it. Invest in low cost items that will inevitably gain value in later patches. Nature resist potions for AQ, etc. This is the most predictable way to make gold but is a long term investment.
So how does a healer make gold? Having a plan and executing. There are TONS of methods to make gold. Several I use that I did not mention above. Don't wait until you need gold, make a plan now. Don't pinch pennies and stow away your gold for a rainy day, it constantly depreciates on a server. Invest your gold early and watch it payout massively in the long run.
Normally you get a lot of gold as a passive priest. I'm thinking about doing a guide for priest farming, because it's so hard to do that.
There are just some variations you do solo/duo and so on, as I said maybe I make a video on the weekend.
Twitch Channel, feel free to take a look :)!