Elves- A second puberty?

[Eönwë]

Well, I know this sounds strange, but I've been thinking about this for a while now.

Well, I started thinking about Cirdan (you know, a bearded mariner who is a first generation elf, probably over 15000 years old). Just why does he have a beard? Is it because he just has a genetic disorder (or some rare genes)? Or is there another reason- Was it because he was old?

Well, we know that Elrond was very old, and is described as such:

Originally Posted by fotr

The face of Elrond was ageless, neither old nor young…his hair was dark…[he was] hale as a tried warrior in the fullness of his strength

Whereas Cirdan:

Originally Posted by rotk

His beard was long, and he was grey and old

I was thinking that maybe after their 10000th year, elves stop being so youthful, and start getting grey. Even after however many years Elrond lived, he had black hair. But Cirdan was far older, and was going grey, and what I am saying is that maybe when they get to a certain age, elves get a beard.

After all, Cirdan is the oldest elf left in Middle Earth (that we are told about) so we have no-one to compare him to. And even if the first generation elves in Aman have not grown grey and bearded, that may be because they are in the Blessed Realm, the Immortal Land, where things do not grow old.

Is there anything in the works of Tolkien that mention anything about this or am I just picking at nonexistent ideas? And does anyone know of other bearded elves?