This achievement may take years (literally) to achieve if you don't have any of the pets yet. You must be level 60+ to acquire the Orphan quest in Shatt.

Alliance Levels 60+

First you must visit Orphan Matron Mercy in Lower City, Shattrah to pick up the Draenei Orphan Whistle.

• A Trip to the Dark Portal: Dornaa would like to be taken to the Dark Portal atop the Stair of Destiny! This is simple - you can take the gryphon to the Dark Portal or go there on your flying mount. Stand in front of the portal in the middle!
• Auchindoun and the Ring of Observance: You need to take her to the Auchindoun summoning stone in the Bone Wastes. This where the instances Mana-Tombs, Shadow Labyrinth and Sethekk Halls are located. You can fly to Allerian Stronghold and walk or use your flying mount. The stone is pretty hard to miss!
• Jheel is at Aeris Landing!: Aww how cute, Dornaa wants to visit her brother Jheel! He's located at Aeris Landing right next to the Spirit Fields in Nagrand. The coordinates are 31,57.
• The Seat of the Naaru: Your orphan wants to visit O'ros at the Seat of the Naaru. O'ros looks like A'dal from Shattrah and is located at the bottom of the Seat of the Naaru. This is one of the out of the way quests. You can easily take the portal from Shattrah to Exodar, but make sure you have your hearthstone so you can return to the Outlands. Otherwise, you will have a long trip back through the Dark Portal.
• Time to Visit the Caverns: Another out of the way quest. Dornaa asks to visit the Caverns of Time and see Zaladormu the dragon located in the middle. She also asks that you buy her a Toy Dragon which can be purchased from the Keepers of Time Quartermaster. If you are Honored with the Keepers of Time you can teleport there from the World's End Tavern in Lower City, otherwise take the boat to Theramore and fly over to Tanaris.

Once you've completed all of these you will receive the Back to the Orphanage quest. Make your way back to Orphan Matron Mercy in Lower City to choose your reward.

Horde Levels 60+

First you must visit Orphan Matron Mercy in Lower City, Shattrah to pick up the Blood Elf Orphan Whistle.

• A Trip to the Dark Portal: Salandria would like to be taken to the Dark Portal atop the Stair of Destiny! This is simple - you can take the gryphon to the Dark Portal or go there on your flying mount. Stand in front of the portal in the middle!
• Hch'uu and the Mushroom People: Your orphan wants to visit with Hch'uu in Sporeggar, Zangarmarsh. His coordinates are 19,51. Just speak with him to complete the quest.
• Now, When I Grow Up...: Apparently Salandria is quite a fan of Sig Nicious of Elite Tauren Chieftain! They will be hanging out in Silvermoon City (which is a little out of the way) on the balcony near the Guild Registrar bulding. She will speak with them from below so there's no need to try and find a way up to the balcony.
• Visit the Throne of the Elements: Take Salandria to the Throne of Elements in Nagrand and speak with Elementalist Sharvak. The Throne is located around 60,22.
• Time to Visit the Caverns: Another out of the way quest. Dornaa asks to visit the Caverns of Time and see Zaladormu the dragon located in the middle. She also asks that you buy her a Toy Dragon which can be purchased from the Keepers of Time Quartermaster. If you are Honored with the Keepers of Time you can teleport there from the World's End Tavern in Lower City.

Once you've completed all of these you will receive the Back to the Orphanage quest. Make your way back to Orphan Matron Mercy in Lower City to choose your reward.