So,
1. The dove is domestic. It grown from squab to adolescent in the bird house and have mark «domestic» in the tooltip, when I hovering mouse.
2. I tried to right click with key on dove (it is in my inventory)
3. I tried with official client and Ender`s. Same result.
4. I asked players, and one told me, all works fine for his doves.
5. No items attached, because te only one option of dove only is «Wring neck»
Birdhouse is inside village claim. Dove returns to it.
So looks like a bug.