Aye, there is no specific board for eagles, or "extras" that aren't quite canine or feline. We could consider making an Misc. Mate Search board, however, I don't think there is enough demand for non-feline/canine characters in those boards for it to branch off as such.
Perhaps, you could try posting it in a board, for what model you use for your eagle? If you use a canine model, you could post it in canines, or the same for felines.
I hope this was helpful. ^^