Oh, right!

I've been leveling a Balance Druid! She's level 20!
That was the fastest level 20 I've ever done. I blew through the Worgen starting zone with heirlooms, although I always need help with the spidery bits, because they're ALL SPINDELYS.
I did 14-15 with a couple quests in Darkshore, and then after that I started queueing for dungeons while I quested. Got into a couple dungeons with good groups, and the time flew by. Was leveling really quickly, even though I barely had time to quest in-between groups!

So this is my lovely Druid, Elzabethi.

Gear right now:

Preened Tribal War Feathers, Patched Leather Shoulders, Ancient Bloodmoon Cloak, Paramedic Bracers, Serpentis Gloves, Vigorous Belt of Vision, Preened Wildfeather Leggings, Seer's Boots, Medicine Staff of Intellect

Also, is it just a thing that Balance Druids do lower DPS than others? Or is that just me? There was one dungeon where I was doing top DPS, but I also think I was the highest level in there...

It feels like sometimes I don't have time to fire off anything besides Moonfire/Sunfire. And half the time I absolutely dread Lunar Eclipse because it means I won't get time to attack because Starfire takes forever to cast! I do fine when I'm in Solar Eclipse, but Lunar Eclipse is just...ugh. Starsurge is nice though. Does it get better when I get Starfall?

Once I've established which side my eclipses are going first by using Starsurge (which I believe is heading towards Solar by default?)...let's assume it's headed towards Solar Eclipse...I cast Moonfire and then spam Starfire (well, I say spam, but in dungeons it's more like "attempt to cast"). Do this for every enemy until I hit Solar Eclipse. And then for normal enemies it's Sunfire > Wrath spam until I'm out of Eclipse. Then Sunfire > Wrath/Starsurge spam until Lunar. Rinse and repeat.
For bosses I apply both Sunfire and Moonfire and keep them up, and then just use the applicable Eclipsey moves. I try to use Astral Communion before boss fights to be in Eclipse form before it begins, although it doesn't seem to matter much.

Now, as you probably know, I know next to nothing about DPS because all I ever do is heal or quest. Do I worry about Faerie Fire? How do I know it's a good time to interrupt/silence with Solar Beam?

That said, I'm excited for a couple new abilities that I've never used before because I've never gotten past level 30 as a Druid (let alone Balance druid). Starfall for one. It sounds pretty. :)
Euphoria sounds useful. Barkskin sounds incredibly useful. I can't even wait for Flight Form. Celestial Alignment sounds really nice. Mastery: Total Eclipse is exciting.  Wild Mushroom looks adorable.