So, thanks to Nyjin on the forums, we have found the Orobird (Or well, one of them at least). It is, indeed, in Alderaan. At the bridge in the Serene Meadow in Alsakan Lowlands. Coordinates are: X: 140, Y: 1810, Z: 209.
Walk next to the lower part of the bridge and position yourself right on top of the straight horizontal log. Jump down onto it and then run across it. Then, jump down to the nest below it. The Orobird Egg appears a little before the egg that is always in the nest.
It IS on a cooldown that lasts 8 hours. (Edit: May have changed to 4 hours on the Live server)
I received an Unusual Egg.
It’s possible that the egg is random (you can see what kind it is when you hover over it). This location will always grant the Unusual Egg.
There is still at least 1, most likely 2 (As there’s also the “Wonderous” and “Mysterious” eggs according to databases) so let’s up they are found soon!
(Edit: Hatching Guide here!)