Where is eaglet on HorseIsle?

You will never meet Eaglet.

To start the quest "Eaglets' Dinner(100qp) [Novice]"
you'll have to complete the quest "Anabelle's Nest".
Anabelle is on Vine Isle. Complete her nest quest, and return to her. She'll ask you to find some food or her eaglets, which will start the quest "Eaglets' Dinner".