The best way to RP a dragon...
Don't do it. Most people won't like it, it's sketchy with lore, and near impossible to do well. The Warcraft universe is an interesting place, there is plenty to do without making your characters a demon, or a dragon, or a San'layn. Personal opinions aside, many dragon RPers have been 'chased' off the server by people refusing to RP with them or correcting their lore, Horde side.
As for our population, yes, it is smaller. There is walk-up RP to be found, but don't expect it to be the main source of RP, or abundant, considering if you're coming from WrA or ER. A good way to promote RP is to join the IC channels on either Alliance, or Horde, or the OOC channels.
I'm not sure about A-side, but what Araceli said isn't too far off about Horde-side. We don't have a ton of 'pure' RP guilds, as even a guild like Razortalons is technically a raiding guild, even if most our members RP. Many people are in guilds such as this, or even quieter RPers that aren't in any of the channels or in RP guilds. We have a fairly consistent community, but it isn't too large. I'm not so sure about 'elitist', but for the most part, people like to stick to the lore, hence the Dragon RPers leaving.
Which, well, if you're leaving WrA, might be what you're looking for.
Edit: I pointed it out a few times, but for someone skimming the post, this is based off of Horde side observations. I haven't played Alliance for more than a few minutes in over half a year.
Edited by Arothand on 6/26/2011 10:07 PM PDT