Post by Nulgar
There are Transmogrifier NPCs in
Orgrimmar and
Stormwind as well.
Post by Rankkor
There are also Transmog guys in Stormwind, and I imagine in Ogrimmar, in the same place you reforge your gear. Not sure if there is a level requirement- the lowest toon I transmogged was 60-something I think.
To add to what she said:
You can transmog your gear in Stormwind, Orgrimmar, and the 2 shrines in Pandaria. There is no level requirement for it, BUT there is a requirement. You need to be able to equip the item you are mogging.
Example, you have this heirloom
Grand Champion Herod's Shoulder and you want to transmog it to look like this
Barbaric Iron Shoulders, that specific shoulder requires lvl 27, so you need to be lvl 27 to transmog your heirloom into those shoulders.
If you want the heirloom to look like
Masterwork Pauldrons you need to be 58. In other words, you need to be as high a level as to equip the item you want your shoulders to look like.
This is why you don't see lvl 12 characters with their heirlooms transmogged to look like the season 12 crafted pvp pieces. (Those pieces require lvl 90 to be used)
Post by Nulgar
There are some nice sets from
level 30-60 quests added in Cataclysm, and since you won't replace your heirlooms until 80/85, transmogging them isn't really a question of cost or effort (besides obtaining the sets, which are sometimes scattered across several zones)