A nice light tale of the peaceful days of Gondolin.
I am a little uncertain what you mean by "Begatting Day" as it is problematic on several levels.
Firstly the tense is wrong. Begat only belongs as a past tense, as in the biblical "Abraham begat Isaac" sense. Begetting would be more correct.
Secondly is the meaning. As a verb "to beget" is best translated as "to conceive" A Begetting Day would thus be a celebration of the conception of the person involved. I know that elves are different, but not that different.
Finally, and this is a bit picky, but how often would the Eldar consider it worth having an anniversary? Every coronar? It would be a bit repetitive for them, don't you think? The anniversary worth celebrating would only occur every yen (144 coronar). And probably their birth day or naming day, rather than the date of their conception. ;-)