* cucualle (small dove) has been used by Helge Fauskanger in his Bible translation for turtledove. The turtledove is indeed smaller and more slender than the normal dove.
Turtle dove comes from Latin turtur by dissimilation. Since this is both onomatopoeic and in accordance with Quenya phonology, one might just use *turtur in Quenya. (I see that Welsh uses turtur without any changes.)
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