You Don't see Elven Children in LotR because Elves are the eldar race and are leaving Middle Earth.
They mature by age 50 and marry usually no younger than 100. They mature differently than Human children; slower physically, faster mentally.
They concieve and give Birth the same way Humans do, though, Elven Pregnancy is 12 months rahter than 9. Elves usually concieve on their wedding night and give birth on their 1st anniversary. They usually have only one or two children because they must give up a piece of their own Fea (spirit) to pro-create.
Here is a link to another such discussion.
Elven Children Birdland had an interesting thought on this thread you may want to read.
And here's another about Elven life cycles.
The Science of Middle Earth And
Elven Pregnancy
Hope this answers your questions.
[ November 11, 2002: Message edited by: Raefindel ]